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tomleslie

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Makes no sense...

tomleslie 13876
September 21 2020
0 0

@janhardo 

I have just run the worksheet  R-90_Animated_Trace_of_a_Curve_Drawn_by_Radius_Vector.mw posted by rlopez: see the output in the worksheet below

anim2.mw

which works perfectly. I can only think of two possibilities for your problem

  1. You are not running the same worksheet. This is simple to check
    1. Run your worksheet demonstrating the problem
    2. Save your worksheet (with output)
    3. Upload the saved worksheet here using the big green up-arrow in the Mapleprimes toolbar
    4. That way we all get see exactkly what is failing and where - this is useful information
  2. Maple version issue: you have not specified which Maple version you are using.- do so!

 

Be clear...

tomleslie 13876
September 21 2020
0 0

@janhardo 

There is no attached worksheet???? Did you mean to attach one??

Usually(?) when one gets the message 

    [Length of output exceeds limit of 1000000]

after trying to produce an animation, it means that you have successfully produced the data for a lot of plot stuctures, but have not successfully passed these to either an animate() or display(...,insequence=true) command. So Maple attempts to output the data for all of the plot structures - which can be a *lot* of data!!

Use...

tomleslie 13876
September 16 2020
0 0

the big green up-arrow in the Mapleprimes toolbar to upload your worksheet

What can be plotted...

tomleslie 13876
September 14 2020
0 0

@Madhukesh J K 

As you have been told many times before, in order to completely evaluate the expressions you want, values are required for the variables Re and Cf

Without this information, all that can be meaning plotted are the values of the quantities

R__e^(-0.5)*sh
R__e^(-0.5)*NU
R__e^(0.5)*C__f

whihc is done in the attached


 

> 

  restart:
> 

  ODES := diff(f(eta), eta$4)+(2*f(eta)*diff(f(eta), eta$3)+2*g(eta)*diff(g(eta), eta))*(1-phi)^2.5*(1-phi+phi*rhos/rhof)-sigmanf*M*(diff(f(eta), eta$2))*(1-phi)^2.5/sigmaf = 0,
          diff(g(eta), eta$2)-(1-phi)^2.5*(1-phi+phi*rhos/rhof)*(2*(diff(f(eta), eta))*g(eta)-2*(diff(g(eta), eta))*f(eta))-sigmanf*M*g(eta)*(1-phi)^2.5/sigmaf = 0,
           k[nf]*diff(theta(eta), eta$2)/(Pr*k[f])+((1-phi+phi*rhos*cps/(rhof*cpf))*2)*f(eta)*(diff(theta(eta), eta))-4*lambda*(1-phi+phi*rhos*cps/(rhof*cpf))*(f(eta)^2*diff(theta(eta), eta$2)+f(eta)*diff(f(eta), eta)*diff(theta(eta), eta))+sigmanf*M*Ec*(diff(f(eta), eta)^2+g(eta)^2)/sigmaf = 0,
          (1-phi)^2.5*(diff(chi(eta), eta$2))+2*Sc*f(eta)*(diff(chi(eta), eta))-sigma*Sc*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta)))*chi(eta) = 0:
> 

  bcs:= f(0) = 0,
        D(f)(0) = A1+gamma1*((D@@2)(f))(0),
        f(10) = 0,
        D(f)(10) = 0,
        g(0) = 1+gamma2*(D(g))(0),
        g(10) = 0,
        theta(0) = 1+gamma3*(D(theta))(0),
        theta(10) = 0,
        chi(0) = 1,
        chi(10) = 0:
> 

  params:=[ lambda = 0.1e-1, sigma = .1, Ec = .2, E = .1, M = mv,
            delta = .1, n = .1, Sc = 3, A1 = .5, gamma1 = .5,
            gamma2 = .5, gamma3 = .5, Pr = 6.2, phi = pVal,
            rhos = 5.06*10^3, rhof = 997, cps = 397.21, cpf = 4179,
            k[nf] = .6358521729, k[f] = .613, sigmanf = 0.5654049962e-5,
            sigmaf = 5.5*10^(-6)
          ]:
> 

  phiVals:=[0.01, 0.1, 0.2]:
  Mvals:= [3, 5, 7]:
  ans:=Matrix( numelems(Mvals)*numelems(phiVals)+1, 5):
  ans[1,..]:= < 'M' | 'phi' | expr1 | expr2 |expr3>:
  for k from 1 by 1 to 3 do
      mv:= Mvals[k]:
      for j from 1 by 1 to 3 do
          pVal:=phiVals[j]:
          sol:=dsolve( eval([ODES, bcs], params), numeric, output=listprocedure);
          ans[3*(k-1)+j+1,..]:= `<|>`([ mv,
                                        pVal,
                                        R__e^(-0.5)*sh= eval( -diff(chi(eta), eta),
                                                              [sol[], params[]]
                                                            )(0),
                                        R__e^(-0.5)*NU= eval( -k[nf]/k[f]*diff(theta(eta), eta),
                                                              [sol[], params[]]
                                                            )(0),
                                        R__e^(0.5)*C__f=eval( (diff(f(eta), eta,eta)^2+diff(g(eta), eta)^2)^0.5/(1-phi)^2.5,
                                                             [sol[], params[]]
                                                           )(0)
                                      ]);
      od:
  od:
  ans;

Matrix(10, 5, {(1, 1) = M, (1, 2) = phi, (1, 3) = expr1, (1, 4) = expr2, (1, 5) = expr3, (2, 1) = 3, (2, 2) = 0.1e-1, (2, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .8372457480942863, (2, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .4834054065319601, (2, 5) = `#msub(mi("R"),mi("e"))`^.5*`#msub(mi("C"),mi("f"))` = 1.1046154919037543, (3, 1) = 3, (3, 2) = .1, (3, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = 1.021986261468336, (3, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .4754384577066604, (3, 5) = `#msub(mi("R"),mi("e"))`^.5*`#msub(mi("C"),mi("f"))` = 1.33386654332825, (4, 1) = 3, (4, 2) = .2, (4, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = 1.2941432851078216, (4, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .45407567754906397, (4, 5) = `#msub(mi("R"),mi("e"))`^.5*`#msub(mi("C"),mi("f"))` = 1.6780654526026586, (5, 1) = 5, (5, 2) = 0.1e-1, (5, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .755391808490033, (5, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .339210573029866, (5, 5) = `#msub(mi("R"),mi("e"))`^.5*`#msub(mi("C"),mi("f"))` = 1.2338936646635543, (6, 1) = 5, (6, 2) = .1, (6, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .9208792973290651, (6, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .3286901704724688, (6, 5) = `#msub(mi("R"),mi("e"))`^.5*`#msub(mi("C"),mi("f"))` = 1.4899650859151932, (7, 1) = 5, (7, 2) = .2, (7, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = 1.1758533608836694, (7, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .30017146961027347, (7, 5) = `#msub(mi("R"),mi("e"))`^.5*`#msub(mi("C"),mi("f"))` = 1.8741184958791277, (8, 1) = 7, (8, 2) = 0.1e-1, (8, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .7099105772331517, (8, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .23556393087742236, (8, 5) = `#msub(mi("R"),mi("e"))`^.5*`#msub(mi("C"),mi("f"))` = 1.3221775421017348, (9, 1) = 7, (9, 2) = .1, (9, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .8604441059913419, (9, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .2210983023715746, (9, 5) = `#msub(mi("R"),mi("e"))`^.5*`#msub(mi("C"),mi("f"))` = 1.599725627575632, (10, 1) = 7, (10, 2) = .2, (10, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = 1.0979554105884857, (10, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .18651469675648197, (10, 5) = `#msub(mi("R"),mi("e"))`^.5*`#msub(mi("C"),mi("f"))` = 2.0166245409320913})

 (1)
> 

 for k from 1 by 1 to 3 do
      plot( [ seq( [ seq( [ans[j,1], rhs(ans[j,2+k]) ], j=i..10,3 ) ], i=2..4 ) ],
            color=[red, green, blue],
            labels=[typeset(M), typeset( lhs(ans[2,2+k]) )],
            labelfont=[times, bold, 20],
            legend=[typeset(phi=0.01),typeset(phi=0.1),typeset(phi=0.2)],
            legendstyle=[font=[times, bold, 20]],
            title=typeset( ans[1,2+k], " versus ", M, " parameterized by ", phi),
            titlefont=[times, bold, 24]
          )
 od;

 

 

 
> 

 


 

Download solODE6.mw

Without plots...

tomleslie 13876
September 12 2020
0 0

@a_simsim 

see the attached


 

restart

QX := ExcelTools:-Import("C:/Users/TomLeslie/Desktop/Source.xlsx")

QI := Interpolation:-LinearInterpolation(QX)

Q := proc (tau) if tau::numeric then QI(tau) else 'procname(tau)' end if end proc

T[12] := 23.1481

23.1481

 (1)

T[21] := 5.4537

5.4537

 (2)

T[23] := 9.752

9.752

 (3)

T[32] := 14.9007

14.9007

 (4)

T[34] := 8.8235

8.8235

 (5)

T[43] := 363.7255

363.7255

 (6)

odesys := diff(L[1](t), t) = L[2](t)/T[21]-L[1](t)/T[12], diff(L[2](t), t) = L[1](t)/T[12]-L[2](t)/T[21]+L[3](t)/T[32]-L[2](t)/T[23]+Q(t), diff(L[3](t), t) = L[2](t)/T[23]-L[3](t)/T[32]+L[4](t)/T[43]-L[3](t)/T[34], diff(L[4](t), t) = L[3](t)/T[34]-L[4](t)/T[43]

diff(L[1](t), t) = .1833617544*L[2](t)-0.4320008986e-1*L[1](t), diff(L[2](t), t) = 0.4320008986e-1*L[1](t)-.2859048225*L[2](t)+0.6711094110e-1*L[3](t)+Q(t), diff(L[3](t), t) = .1025430681*L[2](t)-.1804446522*L[3](t)+0.2749326071e-2*L[4](t), diff(L[4](t), t) = .1133337111*L[3](t)-0.2749326071e-2*L[4](t)

 (7)

L[1](0) := 2500.

L[2](0) := 589.

L[3](0) := 900.

L[4](0) := 37100.

ics := L[1](0) = 2500., L[2](0) = 589., L[3](0) = 900., L[4](0) = 37000

L[1](0) = 2500., L[2](0) = 589., L[3](0) = 900., L[4](0) = 37000

 (8)

sol := dsolve([odesys, ics], numeric, known = Q(t))

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 4, (2) = 4, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 65, (19) = 30000, (20) = 0, (21) = 1, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 62.899820297187155, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..4, {(1) = 2500.0, (2) = 589.0, (3) = 900.0, (4) = 37000.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..4, {(1) = .1, (2) = .1, (3) = .1, (4) = .1}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0}, datatype = integer[8]), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..4, {(1) = 2500.0, (2) = 589.0, (3) = 900.0, (4) = 37000.0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = -0.15130839999244472e-3, (2) = 0.1909118749999808e-1, (3) = -.2772552421000114, (4) = .27527536300000577}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = L[1](t), Y[2] = L[2](t), Y[3] = L[3](t), Y[4] = L[4](t)]`; YP[1] := .1833617544*Y[2]-0.4320008986e-1*Y[1]; YP[2] := 0.4320008986e-1*Y[1]-.2859048225*Y[2]+0.6711094110e-1*Y[3]+Q(X); YP[3] := .1025430681*Y[2]-.1804446522*Y[3]+0.2749326071e-2*Y[4]; YP[4] := .1133337111*Y[3]-0.2749326071e-2*Y[4]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = L[1](t), Y[2] = L[2](t), Y[3] = L[3](t), Y[4] = L[4](t)]`; YP[1] := .1833617544*Y[2]-0.4320008986e-1*Y[1]; YP[2] := 0.4320008986e-1*Y[1]-.2859048225*Y[2]+0.6711094110e-1*Y[3]+Q(X); YP[3] := .1025430681*Y[2]-.1804446522*Y[3]+0.2749326071e-2*Y[4]; YP[4] := .1133337111*Y[3]-0.2749326071e-2*Y[4]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0) ] )) ] ); _y0 := Array(0..4, {(1) = 0., (2) = 2500., (3) = 589., (4) = 900.}); _vmap := array( 1 .. 4, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4) ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch: end try else try procname(procname("right")) catch: end try end if end if end if; return elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch: end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch: end try end if end if end if; return elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, L[1](t), L[2](t), L[3](t), L[4](t)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error end try end proc

 (9)

NULL

> 

#
# OP will have to change the target filename in the following
#  
  ExcelTools:-Export( Matrix( [ lhs~(sol(0)),
                                seq( rhs~(sol(j)), j=0..400,2)
                              ]
                            ),
                      "C:/Users/TomLeslie/Desktop/testdata.xlsx"
                    );
> 

 

 

NULL

Download compODE4.mw

Obvious answer - Yes...

tomleslie 13876
September 11 2020
0 0

@a_simsim 

but the obvious question is why you woud ever want to transfer data from a *serious* math package to a "non-serious" math package. There is certainly nothing which you can do in Excel, which you can't do in Maple - so why bother to transfer? It just complicates stuff!.

Now if you really, really want to do this, the attached code will produce the attached Excel file - although you will have to change the filepath  in the Maple worksheet to something appropriate for your installation

restart

QX := ExcelTools:-Import("C:/Users/TomLeslie/Desktop/Source.xlsx")

QI := Interpolation:-LinearInterpolation(QX)

Q := proc (tau) if tau::numeric then QI(tau) else 'procname(tau)' end if end proc

T[12] := 23.1481

23.1481

 (1)

T[21] := 5.4537

5.4537

 (2)

T[23] := 9.752

9.752

 (3)

T[32] := 14.9007

14.9007

 (4)

T[34] := 8.8235

8.8235

 (5)

T[43] := 363.7255

363.7255

 (6)

odesys := diff(L[1](t), t) = L[2](t)/T[21]-L[1](t)/T[12], diff(L[2](t), t) = L[1](t)/T[12]-L[2](t)/T[21]+L[3](t)/T[32]-L[2](t)/T[23]+Q(t), diff(L[3](t), t) = L[2](t)/T[23]-L[3](t)/T[32]+L[4](t)/T[43]-L[3](t)/T[34], diff(L[4](t), t) = L[3](t)/T[34]-L[4](t)/T[43]

diff(L[1](t), t) = .1833617544*L[2](t)-0.4320008986e-1*L[1](t), diff(L[2](t), t) = 0.4320008986e-1*L[1](t)-.2859048225*L[2](t)+0.6711094110e-1*L[3](t)+Q(t), diff(L[3](t), t) = .1025430681*L[2](t)-.1804446522*L[3](t)+0.2749326071e-2*L[4](t), diff(L[4](t), t) = .1133337111*L[3](t)-0.2749326071e-2*L[4](t)

 (7)

L[1](0) := 2500.

L[2](0) := 589.

L[3](0) := 900.

L[4](0) := 37100.

ics := L[1](0) = 2500., L[2](0) = 589., L[3](0) = 900., L[4](0) = 37000

L[1](0) = 2500., L[2](0) = 589., L[3](0) = 900., L[4](0) = 37000

 (8)

 

sol := dsolve([odesys, ics], numeric, known = Q(t))

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 4, (2) = 4, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 65, (19) = 30000, (20) = 0, (21) = 1, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 62.899820297187155, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..4, {(1) = 2500.0, (2) = 589.0, (3) = 900.0, (4) = 37000.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..4, {(1) = .1, (2) = .1, (3) = .1, (4) = .1}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0}, datatype = integer[8]), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..4, {(1) = 2500.0, (2) = 589.0, (3) = 900.0, (4) = 37000.0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = -0.15130839999244472e-3, (2) = 0.1909118749999808e-1, (3) = -.2772552421000114, (4) = .27527536300000577}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = L[1](t), Y[2] = L[2](t), Y[3] = L[3](t), Y[4] = L[4](t)]`; YP[1] := .1833617544*Y[2]-0.4320008986e-1*Y[1]; YP[2] := 0.4320008986e-1*Y[1]-.2859048225*Y[2]+0.6711094110e-1*Y[3]+Q(X); YP[3] := .1025430681*Y[2]-.1804446522*Y[3]+0.2749326071e-2*Y[4]; YP[4] := .1133337111*Y[3]-0.2749326071e-2*Y[4]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = L[1](t), Y[2] = L[2](t), Y[3] = L[3](t), Y[4] = L[4](t)]`; YP[1] := .1833617544*Y[2]-0.4320008986e-1*Y[1]; YP[2] := 0.4320008986e-1*Y[1]-.2859048225*Y[2]+0.6711094110e-1*Y[3]+Q(X); YP[3] := .1025430681*Y[2]-.1804446522*Y[3]+0.2749326071e-2*Y[4]; YP[4] := .1133337111*Y[3]-0.2749326071e-2*Y[4]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0) ] )) ] ); _y0 := Array(0..4, {(1) = 0., (2) = 2500., (3) = 589., (4) = 900.}); _vmap := array( 1 .. 4, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4) ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch: end try else try procname(procname("right")) catch: end try end if end if end if; return elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch: end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch: end try end if end if end if; return elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, L[1](t), L[2](t), L[3](t), L[4](t)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error end try end proc

 (9)

p1 := plots:-odeplot(sol, [[t, L[1](t)], [t, L[2](t)], [t, L[3](t)], [t, L[4](t)]], t = 0 .. 400)

  

````

NULL

> 

#
# OP will have to change the target filename in the following
#
  ExcelTools:-Export( `<|>`( plottools:-getdata(p1)[1][3][..,1],
                             seq(plottools:-getdata(p1)[j][3][..,2], j=1..4)
                           ),
                       "C:/Users/TomLeslie/Desktop/testdata.xlsx"
                  );

 

``


Download compODE3.mw

testdata.xlsx

 

So maybe more like...

tomleslie 13876
September 11 2020
0 0

@Madhukesh J K 

the attached


 

> 

  restart:
> 

  ODES := diff(f(eta), eta$4)+(2*f(eta)*diff(f(eta), eta$3)+2*g(eta)*diff(g(eta), eta))*(1-phi)^2.5*(1-phi+phi*rhos/rhof)-sigmanf*M*(diff(f(eta), eta$2))*(1-phi)^2.5/sigmaf = 0,
          diff(g(eta), eta$2)-(1-phi)^2.5*(1-phi+phi*rhos/rhof)*(2*(diff(f(eta), eta))*g(eta)-2*(diff(g(eta), eta))*f(eta))-sigmanf*M*g(eta)*(1-phi)^2.5/sigmaf = 0,
           k[nf]*diff(theta(eta), eta$2)/(Pr*k[f])+((1-phi+phi*rhos*cps/(rhof*cpf))*2)*f(eta)*(diff(theta(eta), eta))-4*lambda*(1-phi+phi*rhos*cps/(rhof*cpf))*(f(eta)^2*diff(theta(eta), eta$2)+f(eta)*diff(f(eta), eta)*diff(theta(eta), eta))+sigmanf*M*Ec*(diff(f(eta), eta)^2+g(eta)^2)/sigmaf = 0,
          (1-phi)^2.5*(diff(chi(eta), eta$2))+2*Sc*f(eta)*(diff(chi(eta), eta))-sigma*Sc*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta)))*chi(eta) = 0:
> 

  bcs:= f(0) = 0,
        D(f)(0) = A1+gamma1*((D@@2)(f))(0),
        f(10) = 0,
        D(f)(10) = 0,
        g(0) = 1+gamma2*(D(g))(0),
        g(10) = 0,
        theta(0) = 1+gamma3*(D(theta))(0),
        theta(10) = 0,
        chi(0) = 1,
        chi(10) = 0:
> 

  params:=[ lambda = 0.1e-1, sigma = .1, Ec = .2, E = .1, M = mv,
            delta = .1, n = .1, Sc = 3, A1 = .5, gamma1 = .5,
            gamma2 = .5, gamma3 = .5, Pr = 6.2, phi = pVal,
            rhos = 5.06*10^3, rhof = 997, cps = 397.21, cpf = 4179,
            k[nf] = .6358521729, k[f] = .613, sigmanf = 0.5654049962e-5,
            sigmaf = 5.5*10^(-6)
          ]:
> 

  phiVals:=[0.01, 0.1, 0.2]:
  Mvals:= [3, 5, 7]:
  ans:=Matrix( numelems(Mvals)*numelems(phiVals)+1, 5):
  ans[1,..]:= < 'M' | 'phi' | expr1 | expr2 |expr3>:
  for k from 1 by 1 to 3 do
      mv:= Mvals[k]:
      for j from 1 by 1 to 3 do
          pVal:=phiVals[j]:
          sol:=dsolve( eval([ODES, bcs], params), numeric, output=listprocedure);
          ans[3*(k-1)+j+1,..]:= < mv |
                                  pVal |
                                  R__e^(-0.5)*sh= eval( -diff(chi(eta), eta), [sol[], params[]])(0) |
                                  R__e^(-0.5)*NU= eval( -k[nf]/k[f]*diff(theta(eta), eta),[sol[], params[]])(0) |
                                  R__e^(0.5)*C[f]=eval( (diff(f(eta), eta,eta)^2+diff(g(eta), eta)^2)^0.5/(1-phi)^2.5, [sol[], params[]])(0)
                                >;
      od:
  od:
  ans;

Matrix(10, 5, {(1, 1) = M, (1, 2) = phi, (1, 3) = expr1, (1, 4) = expr2, (1, 5) = expr3, (2, 1) = 3, (2, 2) = 0.1e-1, (2, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .8372457480942863, (2, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .4834054065319601, (2, 5) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.1046154919037543, (3, 1) = 3, (3, 2) = .1, (3, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = 1.021986261468336, (3, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .4754384577066604, (3, 5) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.33386654332825, (4, 1) = 3, (4, 2) = .2, (4, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = 1.2941432851078216, (4, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .45407567754906397, (4, 5) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.6780654526026586, (5, 1) = 5, (5, 2) = 0.1e-1, (5, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .755391808490033, (5, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .339210573029866, (5, 5) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.2338936646635543, (6, 1) = 5, (6, 2) = .1, (6, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .9208792973290651, (6, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .3286901704724688, (6, 5) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.4899650859151932, (7, 1) = 5, (7, 2) = .2, (7, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = 1.1758533608836694, (7, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .30017146961027347, (7, 5) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.8741184958791277, (8, 1) = 7, (8, 2) = 0.1e-1, (8, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .7099105772331517, (8, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .23556393087742236, (8, 5) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.3221775421017348, (9, 1) = 7, (9, 2) = .1, (9, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = .8604441059913419, (9, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .2210983023715746, (9, 5) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.599725627575632, (10, 1) = 7, (10, 2) = .2, (10, 3) = sh/`#msub(mi("R"),mi("e"))`^.5 = 1.0979554105884857, (10, 4) = NU/`#msub(mi("R"),mi("e"))`^.5 = .18651469675648197, (10, 5) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 2.0166245409320913})

 (1)
> 

 


 

Download solODE5.mw

A couple of points...

tomleslie 13876
September 11 2020
0 0
  1. I tested my code on MAple 2020.1 (ie current version), and Maple 18, which is the oldest version (circa 2014) I can access. I notice that you are using Maple 11 (circa 2000), so there may be version issues
  2. With 500 frames, if you save the worksheet with output included you will generate a really big file ~240MB. This has all sorts of knock-on effects - such as Maple's auto-save function taking noticeable time

Once again...

tomleslie 13876
September 11 2020
0 0

@Madhukesh J K 

You want

Plot Nu vs M for varying phi values

 

M= 3..7

 

phi = 0.01, 0.1 and 0.2

and once again you are using a variable (ie ''M') which occurs nowhere in your system.

It is relatively trivial to evaluate the equations you supplied previously, ie

 

for different values of phi, with the same limitations as I mentioned previously ie quantities such as Re and Cf which ( as far as I can tell ) are nowhere specified,

See the attached

> 

restart:
> 

ODES := diff(f(eta), eta$4)+(2*f(eta)*diff(f(eta), eta$3)+2*g(eta)*diff(g(eta), eta))*(1-phi)^2.5*(1-phi+phi*rhos/rhof)-sigmanf*M*(diff(f(eta), eta$2))*(1-phi)^2.5/sigmaf = 0,
        diff(g(eta), eta$2)-(1-phi)^2.5*(1-phi+phi*rhos/rhof)*(2*(diff(f(eta), eta))*g(eta)-2*(diff(g(eta), eta))*f(eta))-sigmanf*M*g(eta)*(1-phi)^2.5/sigmaf = 0,
         k[nf]*diff(theta(eta), eta$2)/(Pr*k[f])+((1-phi+phi*rhos*cps/(rhof*cpf))*2)*f(eta)*(diff(theta(eta), eta))-4*lambda*(1-phi+phi*rhos*cps/(rhof*cpf))*(f(eta)^2*diff(theta(eta), eta$2)+f(eta)*diff(f(eta), eta)*diff(theta(eta), eta))+sigmanf*M*Ec*(diff(f(eta), eta)^2+g(eta)^2)/sigmaf = 0,
        (1-phi)^2.5*(diff(chi(eta), eta$2))+2*Sc*f(eta)*(diff(chi(eta), eta))-sigma*Sc*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta)))*chi(eta) = 0;

diff(diff(diff(diff(f(eta), eta), eta), eta), eta)+(2*f(eta)*(diff(diff(diff(f(eta), eta), eta), eta))+2*g(eta)*(diff(g(eta), eta)))*(1-phi)^2.5*(1-phi+phi*rhos/rhof)-sigmanf*M*(diff(diff(f(eta), eta), eta))*(1-phi)^2.5/sigmaf = 0, diff(diff(g(eta), eta), eta)-(1-phi)^2.5*(1-phi+phi*rhos/rhof)*(2*(diff(f(eta), eta))*g(eta)-2*(diff(g(eta), eta))*f(eta))-sigmanf*M*g(eta)*(1-phi)^2.5/sigmaf = 0, k[nf]*(diff(diff(theta(eta), eta), eta))/(Pr*k[f])+2*(1-phi+phi*rhos*cps/(rhof*cpf))*f(eta)*(diff(theta(eta), eta))-4*lambda*(1-phi+phi*rhos*cps/(rhof*cpf))*(f(eta)^2*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta)))+sigmanf*M*Ec*((diff(f(eta), eta))^2+g(eta)^2)/sigmaf = 0, (1-phi)^2.5*(diff(diff(chi(eta), eta), eta))+2*Sc*f(eta)*(diff(chi(eta), eta))-sigma*Sc*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta)))*chi(eta) = 0

 (1)
> 

bcs:= f(0) = 0,
      D(f)(0) = A1+gamma1*((D@@2)(f))(0),
      f(10) = 0,
      D(f)(10) = 0,
      g(0) = 1+gamma2*(D(g))(0),
      g(10) = 0,
      theta(0) = 1+gamma3*(D(theta))(0),
      theta(10) = 0,
      chi(0) = 1,
      chi(10) = 0;

f(0) = 0, (D(f))(0) = A1+gamma1*((D@@2)(f))(0), f(10) = 0, (D(f))(10) = 0, g(0) = 1+gamma2*(D(g))(0), g(10) = 0, theta(0) = 1+gamma3*(D(theta))(0), theta(10) = 0, chi(0) = 1, chi(10) = 0

 (2)
> 

params:=[ lambda = 0.1e-1, sigma = .1, Ec = .2, E = .1, M = 5,
          delta = .1, n = .1, Sc = 3, A1 = .5, gamma1 = .5,
          gamma2 = .5, gamma3 = .5, Pr = 6.2, phi = pVal,
          rhos = 5.06*10^3, rhof = 997, cps = 397.21, cpf = 4179,
          k[nf] = .6358521729, k[f] = .613, sigmanf = 0.5654049962e-5,
          sigmaf = 5.5*10^(-6)
        ];

[lambda = 0.1e-1, sigma = .1, Ec = .2, E = .1, M = 5, delta = .1, n = .1, Sc = 3, A1 = .5, gamma1 = .5, gamma2 = .5, gamma3 = .5, Pr = 6.2, phi = pVal, rhos = 5060.00, rhof = 997, cps = 397.21, cpf = 4179, k[nf] = .6358521729, k[f] = .613, sigmanf = 0.5654049962e-5, sigmaf = 0.5500000000e-5]

 (3)
> 

phiVals:=[0.01, 0.1, 0.2]:
ans:=Matrix( numelems(phiVals), 4):
for j from 1 by 1 to 3 do
    pVal:=phiVals[j]:
    sol:=dsolve( eval([ODES, bcs], params), numeric, output=listprocedure);
    ans[j,..]:=<pVal |
                R__e^(-0.5)*sh= eval( -diff(chi(eta), eta), [sol[], params[]])(0) |
                R__e^(-0.5)*NU= eval( -k[nf]/k[f]*diff(theta(eta), eta),[sol[], params[]])(0) |
                R__e^(0.5)*C[f]=eval( (diff(f(eta), eta,eta)^2+diff(g(eta), eta)^2)^0.5/(1-phi)^2.5, [sol[], params[]])(0)
              >;
od:
ans;

Matrix(3, 4, {(1, 1) = 0.1e-1, (1, 2) = sh/`#msub(mi("R"),mi("e"))`^.5 = .755391808490033, (1, 3) = NU/`#msub(mi("R"),mi("e"))`^.5 = .339210573029866, (1, 4) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.2338936646635543, (2, 1) = .1, (2, 2) = sh/`#msub(mi("R"),mi("e"))`^.5 = .9208792973290651, (2, 3) = NU/`#msub(mi("R"),mi("e"))`^.5 = .3286901704724688, (2, 4) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.4899650859151932, (3, 1) = .2, (3, 2) = sh/`#msub(mi("R"),mi("e"))`^.5 = 1.1758533608836694, (3, 3) = NU/`#msub(mi("R"),mi("e"))`^.5 = .30017146961027347, (3, 4) = `#msub(mi("R"),mi("e"))`^.5*C[f] = 1.8741184958791277})

 (4)
> 

 

Download solODE4.mw

Hmmm...

tomleslie 13876
September 11 2020
0 0

@r66 

Now we have six inconsistent equations in four unknowns.

See the attached

> 

restart;
Digits:=30:
with(LinearAlgebra):
sys := {-.207106781186547524400844362106*lambda[1]+1.20710678118654752440084436211*lambda[2] = 0,

         1.20710678118654752440084436211*x[1]-.207106781186547524400844362106*x[2] = 1,

        -1.61353108866376978508023871599*lambda[1]+1.61353108866376978508023871599*lambda[2]+1.20710678118654752440084436210*x[1]-1.20710678118654752440084436210*lambda[1]-.207106781186547524400844362105*x[2]+.207106781186547524400844362105*lambda[2] = 0,

         1.37455258362134694054214893147*lambda[1]-1.37455258362134694054214893147*lambda[2]-1.41421356237309504880168872421*x[1]+1.41421356237309504880168872421*lambda[1]+1.41421356237309504880168872421*x[2]-1.41421356237309504880168872421*lambda[2] = 0,

        -1.37455258362134694054214893147*x[1]+1.37455258362134694054214893147*x[2]-1.41421356237309504880168872421*x[1]-1.41421356237309504880168872421*lambda[1]+1.41421356237309504880168872421*x[2]+1.41421356237309504880168872421*lambda[2] = 0,

       -.238978505042422844538089784517*x[1]+.238978505042422844538089784517*x[2]+1.20710678118654752440084436210*x[1]+1.20710678118654752440084436210*lambda[1]-.207106781186547524400844362105*x[2]-.207106781186547524400844362105*lambda[2] = 0}:        
 
> 

  A, b:= GenerateMatrix( sys, [x[1], x[2], lambda[1], lambda[2]]):
  Y := LeastSquares(A, b);

Vector(4, {(1) = .353705468156612767557359017902, (2) = .345114844319696165524575353156, (3) = -0.102337307257419522240006385393e-1, (4) = -0.501467883879825244178186979966e-1})

 (1)
> 

#
# Idle curiosity, check the "residuals" ie how close is the
# above solution to satisfying the set of equations??
#
  eval(sys, [x[1]=Y[1], x[2]=Y[2], lambda[1]=Y[3], lambda[2]=Y[4]]);

{-0.804028283910858946950090562578e-1 = 0, -0.584130532877222366706375955640e-1 = 0, 0.99159207252167518964591222123e-1 = 0, .293051151052208384874849915111 = 0, .351464204339930621545487510671 = 0, .355484644607860993579662574214 = 1}

 (2)
> 

#
# More idle curiosity - where do these coefficients come from?
#
# Most(?) of them can  be expressed as "simple" algebraic terms
# Maybe, the others can be as well - because the identify()
# command certainly isn't "bullet-proof"
#
  identify~(A);

Matrix(6, 4, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 1/2-(1/2)*sqrt(2), (1, 4) = 1/2+(1/2)*sqrt(2), (2, 1) = 1/2+(1/2)*sqrt(2), (2, 2) = 1/2-(1/2)*sqrt(2), (2, 3) = 0, (2, 4) = 0, (3, 1) = 1/2+(1/2)*sqrt(2), (3, 2) = 1/2-(1/2)*sqrt(2), (3, 3) = -2.82063786985031730948108307809, (3, 4) = 1.82063786985031730948108307810, (4, 1) = -sqrt(2), (4, 2) = sqrt(2), (4, 3) = 2.78876614599444198934383765568, (4, 4) = -2.78876614599444198934383765568, (5, 1) = -2.78876614599444198934383765568, (5, 2) = 2.78876614599444198934383765568, (5, 3) = -sqrt(2), (5, 4) = sqrt(2), (6, 1) = .968128276144124679862754577583, (6, 2) = 0.31871723855875320137245422412e-1, (6, 3) = 1/2+(1/2)*sqrt(2), (6, 4) = 1/2-(1/2)*sqrt(2)})

 (3)
> 

 

Download LSQ.mw

To state the seriously obvious...

tomleslie 13876
September 10 2020
0 0

@Madhukesh J K 

You require

"varying the values of phi2 like 0.1, 0.01, 0.2"

You will observe that the name 'phi2' does not occur anywhere in your problem statement or supplied codes. Varying a non-existent parameter is a rather pointless exercise.

Hopefully you will eventually be able to ask a sensible question

Saying something...

tomleslie 13876
September 10 2020
0 0

@Madhukesh J K 

"But I am trying to draw the graph but not obtaining"

is not helpful.

I have no idea what you are trying to graph, and you seem determined not to explain it.

Don't...

tomleslie 13876
September 10 2020
0 0

@janhardo 

use

with(packageName)

inside a procedure, this will cause an error. The correct syntax is

uses packageName

Or you can always use the "longform" name for any command, eg

plots:-display()

The command 'display3d()' *may* have existed many years ago - but its functionality was perhaps incorporated into the display() command. I wouldn't worry about this so as I siad in my original worksheet

plots:-display3d := proc()
   1   `plots/display`(_passed)
end proc

In other words any use of display3d() will just call display() with the saem arguments

 

Well...

tomleslie 13876
September 10 2020
0 0

@Madhukesh J K 

from the previous sorksheets it is relatively simple to evaluate quantities such as

diff(chi(eta), eta)(0),
diff(theta(eta), eta)(0),
diff(f(eta), eta, eta)(0)
diff(g(eta), eta)(0)

However the equations you supply also contain quantities such as Re and Cf which ( as far as I can tell ) are nowhere specified, so the *best* I can do is shown in the final execution group of the attached


 

> 

restart:
> 

ODES := diff(f(eta), eta$4)+(2*f(eta)*diff(f(eta), eta$3)+2*g(eta)*diff(g(eta), eta))*(1-phi)^2.5*(1-phi+phi*rhos/rhof)-sigmanf*M*(diff(f(eta), eta$2))*(1-phi)^2.5/sigmaf = 0,
        diff(g(eta), eta$2)-(1-phi)^2.5*(1-phi+phi*rhos/rhof)*(2*(diff(f(eta), eta))*g(eta)-2*(diff(g(eta), eta))*f(eta))-sigmanf*M*g(eta)*(1-phi)^2.5/sigmaf = 0,
         k[nf]*diff(theta(eta), eta$2)/(Pr*k[f])+((1-phi+phi*rhos*cps/(rhof*cpf))*2)*f(eta)*(diff(theta(eta), eta))-4*lambda*(1-phi+phi*rhos*cps/(rhof*cpf))*(f(eta)^2*diff(theta(eta), eta$2)+f(eta)*diff(f(eta), eta)*diff(theta(eta), eta))+sigmanf*M*Ec*(diff(f(eta), eta)^2+g(eta)^2)/sigmaf = 0,
        (1-phi)^2.5*(diff(chi(eta), eta$2))+2*Sc*f(eta)*(diff(chi(eta), eta))-sigma*Sc*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta)))*chi(eta) = 0;

diff(diff(diff(diff(f(eta), eta), eta), eta), eta)+(2*f(eta)*(diff(diff(diff(f(eta), eta), eta), eta))+2*g(eta)*(diff(g(eta), eta)))*(1-phi)^2.5*(1-phi+phi*rhos/rhof)-sigmanf*M*(diff(diff(f(eta), eta), eta))*(1-phi)^2.5/sigmaf = 0, diff(diff(g(eta), eta), eta)-(1-phi)^2.5*(1-phi+phi*rhos/rhof)*(2*(diff(f(eta), eta))*g(eta)-2*(diff(g(eta), eta))*f(eta))-sigmanf*M*g(eta)*(1-phi)^2.5/sigmaf = 0, k[nf]*(diff(diff(theta(eta), eta), eta))/(Pr*k[f])+2*(1-phi+phi*rhos*cps/(rhof*cpf))*f(eta)*(diff(theta(eta), eta))-4*lambda*(1-phi+phi*rhos*cps/(rhof*cpf))*(f(eta)^2*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta)))+sigmanf*M*Ec*((diff(f(eta), eta))^2+g(eta)^2)/sigmaf = 0, (1-phi)^2.5*(diff(diff(chi(eta), eta), eta))+2*Sc*f(eta)*(diff(chi(eta), eta))-sigma*Sc*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta)))*chi(eta) = 0

 (1)
> 

bcs:= f(0) = 0,
      D(f)(0) = A1+gamma1*((D@@2)(f))(0),
      f(10) = 0,
      D(f)(10) = 0,
      g(0) = 1+gamma2*(D(g))(0),
      g(10) = 0,
      theta(0) = 1+gamma3*(D(theta))(0),
      theta(10) = 0,
      chi(0) = 1,
      chi(10) = 0;

f(0) = 0, (D(f))(0) = A1+gamma1*((D@@2)(f))(0), f(10) = 0, (D(f))(10) = 0, g(0) = 1+gamma2*(D(g))(0), g(10) = 0, theta(0) = 1+gamma3*(D(theta))(0), theta(10) = 0, chi(0) = 1, chi(10) = 0

 (2)
> 

params:=[ lambda = 0.1e-1, sigma = .1, Ec = .2, E = .1, M = 5,
          delta = .1, n = .1, Sc = 3, A1 = .5, gamma1 = .5,
          gamma2 = .5, gamma3 = .5, Pr = 6.2, phi = 0.1e-1,
          rhos = 5.06*10^3, rhof = 997, cps = 397.21, cpf = 4179,
          k[nf] = .6358521729, k[f] = .613, sigmanf = 0.5654049962e-5,
          sigmaf = 5.5*10^(-6)
        ];

[lambda = 0.1e-1, sigma = .1, Ec = .2, E = .1, M = 5, delta = .1, n = .1, Sc = 3, A1 = .5, gamma1 = .5, gamma2 = .5, gamma3 = .5, Pr = 6.2, phi = 0.1e-1, rhos = 5060.00, rhof = 997, cps = 397.21, cpf = 4179, k[nf] = .6358521729, k[f] = .613, sigmanf = 0.5654049962e-5, sigmaf = 0.5500000000e-5]

 (3)
> 

sol:=dsolve( eval([ODES, bcs], params), numeric, output=listprocedure);

[eta = proc (eta) local _res, _dat, _solnproc; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); _solnproc := _dat[1]; if member(eta, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(eta, `=`) and member(lhs(eta), ["initial", 'initial']) then if type(rhs(eta), 'list') then _res := _solnproc("initial" = [0, op(rhs(eta))]) else _res := _solnproc("initial" = [1, rhs(eta)]) end if; if type(_res, 'list') then return _res[1] end if elif eta = "sysvars" then return _dat[3] end if; eta end proc, chi(eta) = proc (eta) local res, data, solnproc, `chi(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `chi(eta)` := pointto(data[2][2]); return ('`chi(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[2] catch: error end try end proc, diff(chi(eta), eta) = proc (eta) local res, data, solnproc, `diff(chi(eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(chi(eta),eta)` := pointto(data[2][3]); return ('`diff(chi(eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[3] catch: error end try end proc, f(eta) = proc (eta) local res, data, solnproc, `f(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `f(eta)` := pointto(data[2][4]); return ('`f(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[4] catch: error end try end proc, diff(f(eta), eta) = proc (eta) local res, data, solnproc, `diff(f(eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(f(eta),eta)` := pointto(data[2][5]); return ('`diff(f(eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[5] catch: error end try end proc, diff(diff(f(eta), eta), eta) = proc (eta) local res, data, solnproc, `diff(diff(f(eta),eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(diff(f(eta),eta),eta)` := pointto(data[2][6]); return ('`diff(diff(f(eta),eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[6] catch: error end try end proc, diff(diff(diff(f(eta), eta), eta), eta) = proc (eta) local res, data, solnproc, `diff(diff(diff(f(eta),eta),eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(diff(diff(f(eta),eta),eta),eta)` := pointto(data[2][7]); return ('`diff(diff(diff(f(eta),eta),eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[7] catch: error end try end proc, g(eta) = proc (eta) local res, data, solnproc, `g(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `g(eta)` := pointto(data[2][8]); return ('`g(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[8] catch: error end try end proc, diff(g(eta), eta) = proc (eta) local res, data, solnproc, `diff(g(eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(g(eta),eta)` := pointto(data[2][9]); return ('`diff(g(eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[9] catch: error end try end proc, theta(eta) = proc (eta) local res, data, solnproc, `theta(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `theta(eta)` := pointto(data[2][10]); return ('`theta(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[10] catch: error end try end proc, diff(theta(eta), eta) = proc (eta) local res, data, solnproc, `diff(theta(eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(1..11, {(1) = 18446744074434487326, (2) = 18446744074434487766, (3) = 18446744074434487942, (4) = 18446744074434488118, (5) = 18446744074434488294, (6) = 18446744074434488470, (7) = 18446744074434488646, (8) = 18446744074434488822, (9) = 18446744074434488998, (10) = 18446744074434489174, (11) = 18446744074434489438}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(theta(eta),eta)` := pointto(data[2][11]); return ('`diff(theta(eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[11] catch: error end try end proc]

 (4)
> 

plots:-odeplot( sol,
                [ [eta, theta(eta)],
                  [eta, g(eta)],
                  [eta, f(eta)],
                  [eta, chi(eta)]
                ],
                eta=0..10,
                color=[red, green, blue, black]
              );

 
> 

eqns:= [ R__e^(-0.5)*sh= eval( -diff(chi(eta), eta), [sol[], params[]])(0),
         R__e^(-0.5)*Nu= eval( -k[nf]/k[f]*diff(theta(eta), eta),[sol[], params[]])(0),
         R__e^(0.5)*C[f]=eval( (diff(f(eta), eta,eta)^2+diff(g(eta), eta)^2)^0.5/(1-phi)^2.5, [sol[], params[]])(0)
       ];

[sh/R__e^.5 = HFloat(0.755391808490033), Nu/R__e^.5 = HFloat(0.339210573029866), R__e^.5*C[f] = HFloat(1.2338936646635543)]

 (5)
> 

 


 

Download solODE3.mw

 

Re chi...

tomleslie 13876
September 10 2020
0 0

@tomleslie 

  1. Losing chi(eta) just shows problems of having to cut-and-paste. Fixed version below
  2. I, too, have no idea how to calculate Nussult number or skin friction from the information provided. I assume that both can be represented as functions of eta, theta(eta), g(eta), f(eta), chi(eta)????
> 

restart:
> 

ODES := diff(f(eta), eta$4)+(2*f(eta)*diff(f(eta), eta$3)+2*g(eta)*diff(g(eta), eta))*(1-phi)^2.5*(1-phi+phi*rhos/rhof)-sigmanf*M*(diff(f(eta), eta$2))*(1-phi)^2.5/sigmaf = 0,
        diff(g(eta), eta$2)-(1-phi)^2.5*(1-phi+phi*rhos/rhof)*(2*(diff(f(eta), eta))*g(eta)-2*(diff(g(eta), eta))*f(eta))-sigmanf*M*g(eta)*(1-phi)^2.5/sigmaf = 0,
         k[nf]*diff(theta(eta), eta$2)/(Pr*k[f])+((1-phi+phi*rhos*cps/(rhof*cpf))*2)*f(eta)*(diff(theta(eta), eta))-4*lambda*(1-phi+phi*rhos*cps/(rhof*cpf))*(f(eta)^2*diff(theta(eta), eta$2)+f(eta)*diff(f(eta), eta)*diff(theta(eta), eta))+sigmanf*M*Ec*(diff(f(eta), eta)^2+g(eta)^2)/sigmaf = 0,
        (1-phi)^2.5*(diff(chi(eta), eta$2))+2*Sc*f(eta)*(diff(chi(eta), eta))-sigma*Sc*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta)))*chi(eta) = 0;

diff(diff(diff(diff(f(eta), eta), eta), eta), eta)+(2*f(eta)*(diff(diff(diff(f(eta), eta), eta), eta))+2*g(eta)*(diff(g(eta), eta)))*(1-phi)^2.5*(1-phi+phi*rhos/rhof)-sigmanf*M*(diff(diff(f(eta), eta), eta))*(1-phi)^2.5/sigmaf = 0, diff(diff(g(eta), eta), eta)-(1-phi)^2.5*(1-phi+phi*rhos/rhof)*(2*(diff(f(eta), eta))*g(eta)-2*(diff(g(eta), eta))*f(eta))-sigmanf*M*g(eta)*(1-phi)^2.5/sigmaf = 0, k[nf]*(diff(diff(theta(eta), eta), eta))/(Pr*k[f])+2*(1-phi+phi*rhos*cps/(rhof*cpf))*f(eta)*(diff(theta(eta), eta))-4*lambda*(1-phi+phi*rhos*cps/(rhof*cpf))*(f(eta)^2*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta)))+sigmanf*M*Ec*((diff(f(eta), eta))^2+g(eta)^2)/sigmaf = 0, (1-phi)^2.5*(diff(diff(chi(eta), eta), eta))+2*Sc*f(eta)*(diff(chi(eta), eta))-sigma*Sc*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta)))*chi(eta) = 0

 (1)
> 

bcs:= f(0) = 0,
      D(f)(0) = A1+gamma1*((D@@2)(f))(0),
      f(10) = 0,
      D(f)(10) = 0,
      g(0) = 1+gamma2*(D(g))(0),
      g(10) = 0,
      theta(0) = 1+gamma3*(D(theta))(0),
      theta(10) = 0,
      chi(0) = 1,
      chi(10) = 0;

f(0) = 0, (D(f))(0) = A1+gamma1*((D@@2)(f))(0), f(10) = 0, (D(f))(10) = 0, g(0) = 1+gamma2*(D(g))(0), g(10) = 0, theta(0) = 1+gamma3*(D(theta))(0), theta(10) = 0, chi(0) = 1, chi(10) = 0

 (2)
> 

params:=[ lambda = 0.1e-1, sigma = .1, Ec = .2, E = .1, M = 5,
          delta = .1, n = .1, Sc = 3, A1 = .5, gamma1 = .5,
          gamma2 = .5, gamma3 = .5, Pr = 6.2, phi = 0.1e-1,
          rhos = 5.06*10^3, rhof = 997, cps = 397.21, cpf = 4179,
          k[nf] = .6358521729, k[f] = .613, sigmanf = 0.5654049962e-5,
          sigmaf = 5.5*10^(-6)
        ];

[lambda = 0.1e-1, sigma = .1, Ec = .2, E = .1, M = 5, delta = .1, n = .1, Sc = 3, A1 = .5, gamma1 = .5, gamma2 = .5, gamma3 = .5, Pr = 6.2, phi = 0.1e-1, rhos = 5060.00, rhof = 997, cps = 397.21, cpf = 4179, k[nf] = .6358521729, k[f] = .613, sigmanf = 0.5654049962e-5, sigmaf = 0.5500000000e-5]

 (3)
> 

sol:=dsolve( eval([ODES, bcs], params), numeric);

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = 1.0, (1, 2) = -.7553918084900332, (1, 3) = .0, (1, 4) = .2334023920368901, (1, 5) = -.5331952159262199, (1, 6) = 1.0666085358832018, (1, 7) = .4606533806960827, (1, 8) = -1.0786932386078352, (1, 9) = .836490233004227, (1, 10) = -.3270195339915462, (2, 1) = .7802626532116007, (2, 2) = -.6384289692917822, (2, 3) = 0.5181638531335208e-1, (2, 4) = .11041104670139402, (2, 5) = -.2754223837135831, (2, 6) = .6019394589421233, (2, 7) = .22105558411977877, (2, 8) = -.5171426971478558, (2, 9) = .6873921766226637, (2, 10) = -.5416058012723499, (3, 1) = .5999168177325382, (3, 2) = -.5053783748564951, (3, 3) = 0.7564987353318214e-1, (3, 4) = 0.4787729121294094e-1, (3, 5) = -.1361713478085259, (3, 6) = .3086422873130291, (3, 7) = .10568759615554164, (3, 8) = -.24688732515995462, (3, 9) = .5236519193433755, (3, 10) = -.47614856470179373, (4, 1) = .4578166687351046, (4, 2) = -.387229635451622, (4, 3) = 0.854199243472724e-1, (4, 4) = 0.16961619575176414e-1, (4, 5) = -0.6553460714207052e-1, (4, 6) = .15088452197063004, (4, 7) = 0.5010235075160135e-1, (4, 8) = -.11685201467581083, (4, 9) = .3899041624843489, (4, 10) = -.36039084231017, (5, 1) = .3478735128850313, (5, 2) = -.29173394089069116, (5, 3) = 0.8819747005628419e-1, (5, 4) = 0.19525056076296165e-2, (5, 5) = -0.30862850436357597e-1, (5, 6) = 0.7151514089921737e-1, (5, 7) = 0.2344681907211781e-1, (5, 8) = -0.5459315517129785e-1, (5, 9) = .2896900897004851, (5, 10) = -.2591436410187361, (6, 1) = .263693685149383, (6, 2) = -.2178510164251172, (6, 3) = 0.8750491672217238e-1, (6, 4) = -0.5203651467241312e-2, (6, 5) = -0.14261496930349404e-1, (6, 6) = 0.33115622056551317e-1, (6, 7) = 0.10812222531968053e-1, (6, 8) = -0.25131957398943368e-1, (6, 9) = .21681674136294873, (6, 10) = -.1832660650331429, (7, 1) = .19978156510547093, (7, 2) = -.16205341491655745, (7, 3) = 0.8509999836208872e-1, (7, 4) = -0.8550001681867215e-2, (7, 5) = -0.64902069371492906e-2, (7, 6) = 0.15070770986580224e-1, (7, 7) = 0.4920400565583967e-2, (7, 8) = -0.11417045189161923e-1, (7, 9) = .1643773760957666, (7, 10) = -.12946920393548944, (8, 1) = .15157706304234891, (8, 2) = -.12051005145239105, (8, 3) = 0.818613415095571e-1, (8, 4) = -0.10087202314588269e-1, (8, 5) = -0.29220011966203186e-2, (8, 6) = 0.6778617399366728e-2, (8, 7) = 0.22173774015940935e-2, (8, 8) = -0.5135983508373236e-2, (8, 9) = .12668932390688528, (8, 10) = -0.9213644092785578e-1, (9, 1) = .11535614585131156, (9, 2) = -0.8981083124303749e-1, (9, 3) = 0.7822350914483091e-1, (9, 4) = -0.10783808654056634e-1, (9, 5) = -0.13069284372109746e-2, (9, 6) = 0.3027596433783296e-2, (9, 7) = 0.9931813950193112e-3, (9, 8) = -0.2296338300157273e-2, (9, 9) = 0.9946331383661237e-1, (9, 10) = -0.6637608985531422e-1, (10, 1) = 0.8815898316167894e-1, (10, 2) = -0.671835607356214e-1, (10, 3) = 0.7439738168217738e-1, (10, 4) = -0.11096710416954305e-1, (10, 5) = -0.5825692101459699e-3, (10, 6) = 0.13473844696919393e-2, (10, 7) = 0.4434417919959677e-3, (10, 8) = -0.10234405722810058e-2, (10, 9) = 0.795959760572829e-1, (10, 10) = -0.4855044564816883e-1, (11, 1) = 0.6769922036135717e-1, (11, 2) = -0.5049106549659553e-1, (11, 3) = 0.7048287225727022e-1, (11, 4) = -0.11236578748049664e-1, (11, 5) = -0.25931132940615716e-3, (11, 6) = 0.5987462341729311e-3, (11, 7) = 0.19773182015712826e-3, (11, 8) = -0.45553163502350054e-3, (11, 9) = 0.6489718359668274e-1, (11, 10) = -0.3612061694262786e-1, (12, 1) = 0.5225311855245066e-1, (12, 2) = -0.3814030818095862e-1, (12, 3) = 0.6652646109262192e-1, (12, 4) = -0.11298957084886551e-1, (12, 5) = -0.11537717364255411e-3, (12, 6) = 0.2660136662671531e-3, (12, 7) = 0.881484023229404e-4, (12, 8) = -0.20270790961262271e-3, (12, 9) = 0.53844009915677477e-1, (12, 10) = -0.27365674986990562e-1, (13, 1) = 0.4053966259566583e-1, (13, 2) = -0.28965062028126983e-1, (13, 3) = 0.6254963494757301e-1, (13, 4) = -0.11326748164856385e-1, (13, 5) = -0.5132240841931306e-4, (13, 6) = 0.11829100048671203e-3, (13, 7) = 0.3931069347647314e-4, (13, 8) = -0.9023605834380079e-4, (13, 9) = 0.4538234112816808e-1, (13, 10) = -0.2113132322087703e-1, (14, 1) = 0.3161313336339617e-1, (14, 2) = -0.2211839135678929e-1, (14, 3) = 0.5856274002404545e-1, (14, 4) = -0.11339113697397738e-1, (14, 5) = -0.22780698355201957e-4, (14, 6) = 0.527861954863507e-4, (14, 7) = 0.1754468669635701e-4, (14, 8) = -0.4020013292146885e-4, (14, 9) = 0.3878081965854632e-1, (14, 10) = -0.16643543930619925e-1, (15, 1) = 0.2477522321994683e-1, (15, 2) = -0.16985629156990204e-1, (15, 3) = 0.5457109428594684e-1, (15, 4) = -0.11344583424876825e-1, (15, 5) = -0.9980029944747356e-5, (15, 6) = 0.2389279826573239e-4, (15, 7) = 0.783898597381907e-5, (15, 8) = -0.17928908248419424e-4, (15, 9) = 0.3352774450498556e-1, (15, 10) = -0.1338004136750565e-1, (16, 1) = 0.1950860011964993e-1, (16, 2) = -0.13119493061674236e-1, (16, 3) = 0.50577361849542445e-1, (16, 4) = -0.11346929386542587e-1, (16, 5) = -0.40685787494057e-5, (16, 6) = 0.11499925283475425e-4, (16, 7) = 0.3507034202134018e-5, (16, 8) = -0.8006558480480428e-5, (16, 9) = 0.29260924305376496e-1, (16, 10) = -0.1098517027114212e-1, (17, 1) = 0.15428866290865078e-1, (17, 2) = -0.10193679945153284e-1, (17, 3) = 0.4658276465561683e-1, (17, 4) = -0.1134777190197515e-1, (17, 5) = -0.980861480649423e-6, (17, 6) = 0.6971274179109028e-5, (17, 7) = 0.15711742680530185e-5, (17, 8) = -0.35804870904029342e-5, (17, 9) = 0.2572100230824068e-1, (17, 10) = -0.9214622751261432e-2, (18, 1) = 0.1224947113318527e-1, (18, 2) = -0.7969481783930537e-2, (18, 3) = 0.4258782867307486e-1, (18, 4) = -0.11347703911228834e-1, (18, 5) = 0.13746641242656001e-5, (18, 6) = 0.7098931603655314e-5, (18, 7) = 0.7048919878310648e-6, (18, 8) = -0.1603438269767282e-5, (18, 9) = 0.22719990763770282e-1, (18, 10) = -0.7899137836452965e-2, (19, 1) = 0.9755934241204032e-2, (19, 2) = -0.6271688345132486e-2, (19, 3) = 0.38592888997920266e-1, (19, 4) = -0.113467100325686e-1, (19, 5) = 0.4545749591477982e-5, (19, 6) = 0.118205937601639e-4, (19, 7) = 0.31669111084041197e-6, (19, 8) = -0.7190807239302985e-6, (19, 9) = 0.20119794230741537e-1, (19, 10) = -0.69204844950185185e-2, (20, 1) = 0.7786879840551712e-2, (20, 2) = -0.4971190254457108e-2, (20, 3) = 0.3459840263263647e-1, (20, 4) = -0.11344175361833334e-1, (20, 5) = 0.1056509981149292e-4, (20, 6) = 0.2408139499716712e-4, (20, 7) = 0.14248418439322237e-6, (20, 8) = -0.32293942969281773e-6, (20, 9) = 0.17817379792226615e-1, (20, 10) = -0.6195449390288176e-2, (21, 1) = 0.6220150137555235e-2, (21, 2) = -0.3972474821037372e-2, (21, 3) = 0.3060524381266614e-1, (21, 4) = -0.11338501810675986e-1, (21, 5) = 0.23267532605780347e-4, (21, 6) = 0.5168600092227659e-4, (21, 7) = 0.6419790337601151e-7, (21, 8) = -0.1452410499215291e-6, (21, 9) = 0.15734484198507405e-1, (21, 10) = -0.5665108178588169e-2, (22, 1) = 0.4962639939873149e-2, (22, 2) = -0.32046445745686153e-2, (22, 3) = 0.26615194922336032e-1, (22, 4) = -0.11326090748731244e-1, (22, 5) = 0.5075760151999344e-4, (22, 6) = 0.11231433524621879e-3, (22, 7) = 0.2896717381817158e-7, (22, 8) = -0.6541738924513076e-7, (22, 9) = 0.13810417515664829e-1, (22, 10) = -0.5287568137742678e-2, (23, 1) = 0.3942827458445932e-2, (23, 2) = -0.2614952994225411e-2, (23, 3) = 0.22631976455084163e-1, (23, 4) = -0.11299038409557675e-1, (23, 5) = 0.11063056483977635e-3, (23, 6) = 0.2449530094232462e-3, (23, 7) = 0.13089599767721546e-7, (23, 8) = -0.295085008006464e-7, (23, 9) = 0.1199699257502044e-1, (23, 10) = -0.5032959787256627e-2, (24, 1) = 0.31052352214619924e-2, (24, 2) = -0.2164129316512358e-2, (24, 3) = 0.1866341976475459e-1, (24, 4) = -0.11240052514691031e-1, (24, 5) = 0.24134555106518948e-3, (24, 6) = 0.535210032286014e-3, (24, 7) = 0.5923212791579345e-8, (24, 8) = -0.13331258591256416e-7, (24, 9) = 0.10254915505744757e-1, (24, 10) = -0.48798031054340975e-2, (25, 1) = 0.2406323661278666e-2, (25, 2) = -0.18230077998604287e-2, (25, 3) = 0.14726425190813986e-1, (25, 4) = -0.11111283212734687e-1, (25, 5) = 0.5271851889674087e-3, (25, 6) = 0.1171130106309907e-2, (25, 7) = 0.26833656699188345e-8, (25, 8) = -0.60331338961262195e-8, (25, 9) = 0.8551349752183642e-2, (25, 10) = -0.4812029795787041e-2, (26, 1) = 0.18114163605172384e-2, (26, 2) = -0.1570082570172615e-2, (26, 3) = 0.1085804975697051e-1, (26, 4) = -0.10829774465351895e-1, (26, 5) = 0.11531738896899022e-2, (26, 6) = 0.2566268329316885e-2, (26, 7) = 0.12156241599010524e-8, (26, 8) = -0.27376764747381573e-8, (26, 9) = 0.6858584693392237e-2, (26, 10) = -0.4815831708263478e-2, (27, 1) = 0.12923545174057275e-2, (27, 2) = -0.13896978284247828e-2, (27, 3) = 0.71398068657935005e-2, (27, 4) = -0.10213456855523977e-1, (27, 5) = 0.25260684566229966e-2, (27, 6) = 0.56312079091388025e-2, (27, 7) = 0.5478719193333531e-9, (27, 8) = -0.125165303730281e-8, (27, 9) = 0.5154022756114182e-2, (27, 10) = -0.4875180085166705e-2, (28, 1) = 0.8256861486562427e-3, (28, 2) = -0.12706447859419103e-2, (28, 3) = 0.3750824320492574e-2, (28, 4) = -0.8862204648218151e-2, (28, 5) = 0.5541136862038557e-2, (28, 6) = 0.12372629045343425e-1, (28, 7) = 0.2395597574335643e-9, (28, 8) = -0.5898056478931165e-9, (28, 9) = 0.3422138788700792e-2, (28, 10) = -0.4964684607128678e-2, (29, 1) = 0.3919112108734191e-3, (29, 2) = -0.12049837188478894e-2, (29, 3) = 0.10877174273982045e-2, (29, 4) = -0.5901778454769809e-2, (29, 5) = 0.12156806678318147e-1, (29, 6) = 0.27182771282895486e-1, (29, 7) = 0.8820788103503235e-10, (29, 8) = -0.31511002859609665e-9, (29, 9) = 0.16618171949916544e-2, (29, 10) = -0.5041399206976267e-2, (30, 1) = .0, (30, 2) = -0.11861731323706884e-2, (30, 3) = .0, (30, 4) = .0, (30, 5) = 0.25360495675570482e-1, (30, 6) = 0.5675696394182005e-1, (30, 7) = .0, (30, 8) = -0.24560414943478344e-9, (30, 9) = .0, (30, 10) = -0.5061752020516661e-2}, datatype = float[8], order = C_order); YP := Matrix(30, 10, {(1, 1) = -.7553918084900332, (1, 2) = .28277765580654185, (1, 3) = .2334023920368901, (1, 4) = -.5331952159262199, (1, 5) = 1.0666085358832018, (1, 6) = -1.6640012559092, (1, 7) = -1.0786932386078352, (1, 8) = 2.5272733396457676, (1, 9) = -.3270195339915462, (1, 10) = -1.638628462313556, (2, 1) = -.6384289692917822, (2, 2) = .4235887041658474, (2, 3) = .11041104670139402, (2, 4) = -.2754223837135831, (2, 5) = .6019394589421233, (2, 6) = -1.2118206800407922, (2, 7) = -.5171426971478558, (2, 8) = 1.211978182506299, (2, 9) = -.5416058012723499, (2, 10) = -0.42178045694081276e-1, (3, 1) = -.5053783748564951, (3, 2) = .4039109898718143, (3, 3) = 0.4787729121294094e-1, (3, 4) = -.1361713478085259, (3, 5) = .3086422873130291, (3, 6) = -.6769894696867113, (3, 7) = -.24688732515995462, (3, 8) = .5779425227353894, (3, 9) = -.47614856470179373, (3, 10) = .34571510253955834, (4, 1) = -.387229635451622, (4, 2) = .3319187825946254, (4, 3) = 0.16961619575176414e-1, (4, 4) = -0.6553460714207052e-1, (4, 5) = .15088452197063004, (4, 6) = -.34277061803120507, (4, 7) = -.11685201467581083, (4, 8) = .2731243553564487, (4, 9) = -.36039084231017, (4, 10) = .3493945462597773, (5, 1) = -.29173394089069116, (5, 2) = .2556933815960436, (5, 3) = 0.19525056076296165e-2, (5, 4) = -0.30862850436357597e-1, (5, 5) = 0.7151514089921737e-1, (5, 6) = -.16490517503327276, (5, 7) = -0.5459315517129785e-1, (5, 8) = .12739397329087432, (5, 9) = -.2591436410187361, (5, 10) = .26889764388092197, (6, 1) = -.2178510164251172, (6, 2) = .19100361654698744, (6, 3) = -0.5203651467241312e-2, (6, 4) = -0.14261496930349404e-1, (6, 5) = 0.33115622056551317e-1, (6, 6) = -0.7681634467376212e-1, (6, 7) = -0.25131957398943368e-1, (6, 8) = 0.5854612838687157e-1, (6, 9) = -.1832660650331429, (6, 10) = .19019736313103375, (7, 1) = -.16205341491655745, (7, 2) = .14064154176376908, (7, 3) = -0.8550001681867215e-2, (7, 4) = -0.64902069371492906e-2, (7, 5) = 0.15070770986580224e-1, (7, 6) = -0.35021510781367615e-1, (7, 7) = -0.11417045189161923e-1, (7, 8) = 0.2655033396162132e-1, (7, 9) = -.12946920393548944, (7, 10) = .13067880603580892, (8, 1) = -.12051005145239105, (8, 2) = .10299547867846623, (8, 3) = -0.10087202314588269e-1, (8, 4) = -0.29220011966203186e-2, (8, 5) = 0.6778617399366728e-2, (8, 6) = -0.15749813972908852e-1, (8, 7) = -0.5135983508373236e-2, (8, 8) = 0.11922646255794004e-1, (8, 9) = -0.9213644092785578e-1, (8, 10) = 0.8920279347603406e-1, (9, 1) = -0.8981083124303749e-1, (9, 2) = 0.7539821061950501e-1, (9, 3) = -0.10783808654056634e-1, (9, 4) = -0.13069284372109746e-2, (9, 5) = 0.3027596433783296e-2, (9, 6) = -0.7027087081197512e-2, (9, 7) = -0.2296338300157273e-2, (9, 8) = 0.5321206144076118e-2, (9, 9) = -0.6637608985531422e-1, (9, 10) = 0.6112942339264841e-1, (10, 1) = -0.671835607356214e-1, (10, 2) = 0.5533137735419787e-1, (10, 3) = -0.11096710416954305e-1, (10, 4) = -0.5825692101459699e-3, (10, 5) = 0.13473844696919393e-2, (10, 6) = -0.31226873201951285e-2, (10, 7) = -0.10234405722810058e-2, (10, 8) = 0.2367322342134213e-2, (10, 9) = -0.4855044564816883e-1, (10, 10) = 0.42263265945813304e-1, (11, 1) = -0.5049106549659553e-1, (11, 2) = 0.40764810113899756e-1, (11, 3) = -0.11236578748049664e-1, (11, 4) = -0.25931132940615716e-3, (11, 5) = 0.5987462341729311e-3, (11, 6) = -0.13852795666094225e-2, (11, 7) = -0.45553163502350054e-3, (11, 8) = 0.10517949915614378e-2, (11, 9) = -0.3612061694262786e-1, (11, 10) = 0.29542521724522118e-1, (12, 1) = -0.3814030818095862e-1, (12, 2) = 0.3017208721361979e-1, (12, 3) = -0.11298957084886551e-1, (12, 4) = -0.11537717364255411e-3, (12, 5) = 0.2660136662671531e-3, (12, 6) = -0.6142148202177792e-3, (12, 7) = -0.20270790961262271e-3, (12, 8) = 0.4671962353811368e-3, (12, 9) = -0.27365674986990562e-1, (12, 10) = 0.208931241779107e-1, (13, 1) = -0.28965062028126983e-1, (13, 2) = 0.2244187023328679e-1, (13, 3) = -0.11326748164856385e-1, (13, 4) = -0.5132240841931306e-4, (13, 5) = 0.11829100048671203e-3, (13, 6) = -0.2722657301039124e-3, (13, 7) = -0.9023605834380079e-4, (13, 8) = 0.20759826760141696e-3, (13, 9) = -0.2113132322087703e-1, (13, 10) = 0.14948096388598689e-1, (14, 1) = -0.2211839135678929e-1, (14, 2) = 0.1677620952260774e-1, (14, 3) = -0.11339113697397738e-1, (14, 4) = -0.22780698355201957e-4, (14, 5) = 0.527861954863507e-4, (14, 6) = -0.12046186955430269e-3, (14, 7) = -0.4020013292146885e-4, (14, 8) = 0.92317781884617e-4, (14, 9) = -0.16643543930619925e-1, (14, 10) = 0.10812897791372093e-1, (15, 1) = -0.16985629156990204e-1, (15, 2) = 0.12604052785493657e-1, (15, 3) = -0.11344583424876825e-1, (15, 4) = -0.9980029944747356e-5, (15, 5) = 0.2389279826573239e-4, (15, 6) = -0.5267131995105059e-4, (15, 7) = -0.17928908248419424e-4, (15, 8) = 0.4109846435475276e-4, (15, 9) = -0.1338004136750565e-1, (15, 10) = 0.7900210375057143e-2, (16, 1) = -0.13119493061674236e-1, (16, 2) = 0.9516145044266379e-2, (16, 3) = -0.11346929386542587e-1, (16, 4) = -0.40685787494057e-5, (16, 5) = 0.11499925283475425e-4, (16, 6) = -0.2157435756074417e-4, (16, 7) = -0.8006558480480428e-5, (16, 8) = 0.1832024688574157e-4, (16, 9) = -0.1098517027114212e-1, (16, 10) = 0.5821378044682933e-2, (17, 1) = -0.10193679945153284e-1, (17, 2) = 0.72185467664174765e-2, (17, 3) = -0.1134777190197515e-1, (17, 4) = -0.980861480649423e-6, (17, 5) = 0.6971274179109028e-5, (17, 6) = -0.5575741160130004e-5, (17, 7) = -0.35804870904029342e-5, (17, 8) = 0.8177887868530999e-5, (17, 9) = -0.9214622751261432e-2, (17, 10) = 0.4316892570752481e-2, (18, 1) = -0.7969481783930537e-2, (18, 2) = 0.5499518741237573e-2, (18, 3) = -0.11347703911228834e-1, (18, 4) = 0.13746641242656001e-5, (18, 5) = 0.7098931603655314e-5, (18, 6) = 0.6276832429213656e-5, (18, 7) = -0.1603438269767282e-5, (18, 8) = 0.3655651714546769e-5, (18, 9) = -0.7899137836452965e-2, (18, 10) = 0.32117654567453435e-2, (19, 1) = -0.6271688345132486e-2, (19, 2) = 0.4205941228020814e-2, (19, 3) = -0.113467100325686e-1, (19, 4) = 0.4545749591477982e-5, (19, 5) = 0.118205937601639e-4, (19, 6) = 0.21859597538587494e-4, (19, 7) = -0.7190807239302985e-6, (19, 8) = 0.16364535058146817e-5, (19, 9) = -0.69204844950185185e-2, (19, 10) = 0.23867234514888805e-2, (20, 1) = -0.4971190254457108e-2, (20, 2) = 0.32265414577900523e-2, (20, 3) = -0.11344175361833334e-1, (20, 4) = 0.1056509981149292e-4, (20, 5) = 0.2408139499716712e-4, (20, 6) = 0.5126639948514238e-4, (20, 7) = -0.32293942969281773e-6, (20, 8) = 0.7336018704245501e-6, (20, 9) = -0.6195449390288176e-2, (20, 10) = 0.17595135095279716e-2, (21, 1) = -0.3972474821037372e-2, (21, 2) = 0.24800054514883675e-2, (21, 3) = -0.11338501810675986e-1, (21, 4) = 0.23267532605780347e-4, (21, 5) = 0.5168600092227659e-4, (21, 6) = 0.11341770267899136e-3, (21, 7) = -0.1452410499215291e-6, (21, 8) = 0.3293378467748498e-6, (21, 9) = -0.5665108178588169e-2, (21, 10) = 0.1272733827559693e-2, (22, 1) = -0.32046445745686153e-2, (22, 2) = 0.19065466694862562e-2, (22, 3) = -0.11326090748731244e-1, (22, 4) = 0.5075760151999344e-4, (22, 5) = 0.11231433524621879e-3, (22, 6) = 0.2483550192242141e-3, (22, 7) = -0.6541738924513076e-7, (22, 8) = 0.14806635625052349e-6, (22, 9) = -0.5287568137742678e-2, (22, 10) = 0.8859221213402465e-3, (23, 1) = -0.2614952994225411e-2, (23, 2) = 0.14619052584558287e-2, (23, 3) = -0.11299038409557675e-1, (23, 4) = 0.11063056483977635e-3, (23, 5) = 0.2449530094232462e-3, (23, 6) = 0.5432833589155546e-3, (23, 7) = -0.295085008006464e-7, (23, 8) = 0.666670981568805e-7, (23, 9) = -0.5032959787256627e-2, (23, 10) = 0.5705285348199399e-3, (24, 1) = -0.2164129316512358e-2, (24, 2) = 0.11130509197357207e-2, (24, 3) = -0.11240052514691031e-1, (24, 4) = 0.24134555106518948e-3, (24, 5) = 0.535210032286014e-3, (24, 6) = 0.11894701963787336e-2, (24, 7) = -0.13331258591256416e-7, (24, 8) = 0.3006004228360561e-7, (24, 9) = -0.48798031054340975e-2, (24, 10) = 0.3070618486734522e-3, (25, 1) = -0.18230077998604287e-2, (25, 2) = 0.8351109386789695e-3, (25, 3) = -0.11111283212734687e-1, (25, 4) = 0.5271851889674087e-3, (25, 5) = 0.1171130106309907e-2, (25, 6) = 0.2607511109869771e-2, (25, 7) = -0.60331338961262195e-8, (25, 8) = 0.13570211862790263e-7, (25, 9) = -0.4812029795787041e-2, (25, 10) = 0.843249746809486e-4, (26, 1) = -0.1570082570172615e-2, (26, 2) = 0.6091823451653341e-3, (26, 3) = -0.10829774465351895e-1, (26, 4) = 0.11531738896899022e-2, (26, 5) = 0.2566268329316885e-2, (26, 6) = 0.5723730261937779e-2, (26, 7) = -0.27376764747381573e-8, (26, 8) = 0.6126940158633967e-8, (26, 9) = -0.4815831708263478e-2, (26, 10) = -0.9866641278186123e-4, (27, 1) = -0.13896978284247828e-2, (27, 2) = 0.42082219403056175e-3, (27, 3) = -0.10213456855523977e-1, (27, 4) = 0.25260684566229966e-2, (27, 5) = 0.56312079091388025e-2, (27, 6) = 0.12580322516418418e-1, (27, 7) = -0.125165303730281e-8, (27, 8) = 0.27529930582226358e-8, (27, 9) = -0.4875180085166705e-2, (27, 10) = -0.22693792665460168e-3, (28, 1) = -0.12706447859419103e-2, (28, 2) = 0.2591755196380921e-3, (28, 3) = -0.8862204648218151e-2, (28, 4) = 0.5541136862038557e-2, (28, 5) = 0.12372629045343425e-1, (28, 6) = 0.2768078349358213e-1, (28, 7) = -0.5898056478931165e-9, (28, 8) = 0.12009759493395973e-8, (28, 9) = -0.4964684607128678e-2, (28, 10) = -0.26109199104091705e-3, (29, 1) = -0.12049837188478894e-2, (29, 2) = 0.11715946041816664e-3, (29, 3) = -0.5901778454769809e-2, (29, 4) = 0.12156806678318147e-1, (29, 5) = 0.27182771282895486e-1, (29, 6) = 0.6087605458274376e-1, (29, 7) = -0.31511002859609665e-9, (29, 8) = 0.4417815964336877e-9, (29, 9) = -0.5041399206976267e-2, (29, 10) = -0.14880072836957918e-3, (30, 1) = -0.11861731323706884e-2, (30, 2) = .0, (30, 3) = .0, (30, 4) = 0.25360495675570482e-1, (30, 5) = 0.5675696394182005e-1, (30, 6) = .1271196477685867, (30, 7) = -0.24560414943478344e-9, (30, 8) = .0, (30, 9) = -0.5061752020516661e-2, (30, 10) = .0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(30, {(1) = .0, (2) = .3136783289704513, (3) = .629333785461503, (4) = .9491161575039805, (5) = 1.2749645188423142, (6) = 1.6076932244647206, (7) = 1.9466940935860562, (8) = 2.290509173258823, (9) = 2.6375736892925463, (10) = 2.986637777249713, (11) = 3.336898797879766, (12) = 3.6878955068213024, (13) = 4.039369533686774, (14) = 4.3911411808783685, (15) = 4.743069265737644, (16) = 5.095066251209129, (17) = 5.447092531955814, (18) = 5.799137312761305, (19) = 6.1511981554805475, (20) = 6.50327122241774, (21) = 6.855348614537765, (22) = 7.207419163320024, (23) = 7.559470747290825, (24) = 7.911500949382626, (25) = 8.26352220504214, (26) = 8.615554115714138, (27) = 8.967610968090243, (28) = 9.319698684610614, (29) = 9.671316610669823, (30) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(30, 10, {(1, 1) = .0, (1, 2) = 0.2824507784916081e-9, (1, 3) = .0, (1, 4) = 0.11148813212264e-9, (1, 5) = 0.22297691915537913e-9, (1, 6) = 0.15118641076234903e-8, (1, 7) = -0.28785358389529936e-10, (1, 8) = -0.57569548139305925e-10, (1, 9) = 0.2322614758957405e-8, (1, 10) = 0.46452296323292086e-8, (2, 1) = -0.1434230937682815e-8, (2, 2) = 0.5592730798061063e-8, (2, 3) = -0.3490753071273115e-8, (2, 4) = 0.8696951735361415e-8, (2, 5) = -0.20400179777004844e-7, (2, 6) = 0.4895400347360599e-7, (2, 7) = -0.64932915782305304e-8, (2, 8) = 0.1542732262979669e-7, (2, 9) = 0.1944251555021743e-8, (2, 10) = 0.66156327068034595e-8, (3, 1) = 0.5953070926919321e-9, (3, 2) = 0.22846276005333153e-10, (3, 3) = -0.9215547919226448e-9, (3, 4) = 0.2239569844628258e-8, (3, 5) = -0.498119288085967e-8, (3, 6) = 0.1189671703853961e-7, (3, 7) = -0.3416655768795502e-8, (3, 8) = 0.8199528360364873e-8, (3, 9) = 0.6046786240824352e-8, (3, 10) = -0.6385009568731916e-8, (4, 1) = 0.7068009785087165e-9, (4, 2) = -0.8627156050361753e-9, (4, 3) = -0.7629366786727266e-12, (4, 4) = -0.4789827792158787e-10, (4, 5) = 0.3250383510122793e-9, (4, 6) = -0.727838956030725e-9, (4, 7) = -0.7202742098656072e-9, (4, 8) = 0.17703630687433924e-8, (4, 9) = 0.4191226344279807e-8, (4, 10) = -0.4809412918399944e-8, (5, 1) = 0.36228568234645206e-9, (5, 2) = -0.3679293572444453e-9, (5, 3) = 0.8820232053075575e-10, (5, 4) = -0.2496153210480705e-9, (5, 5) = 0.6741068562246874e-9, (5, 6) = -0.1528594599362193e-8, (5, 7) = 0.32377403765700695e-9, (5, 8) = -0.735847468420269e-9, (5, 9) = 0.2032268606255743e-8, (5, 10) = -0.8315739353815536e-9, (6, 1) = 0.153566761987036e-9, (6, 2) = -0.2001856273460529e-10, (6, 3) = 0.2406938580400354e-10, (6, 4) = -0.7963227120964935e-10, (6, 5) = 0.21124171182934064e-9, (6, 6) = -0.44865351214625526e-9, (6, 7) = 0.45027014745244277e-9, (6, 8) = -0.10549916312136722e-8, (6, 9) = 0.12106614626179052e-8, (6, 10) = 0.7781744673309872e-9, (7, 1) = 0.8817003207843383e-10, (7, 2) = 0.8253994779642876e-10, (7, 3) = -0.12886138961370127e-10, (7, 4) = 0.16908531855297013e-10, (7, 5) = -0.3592226231601274e-10, (7, 6) = 0.11167354129083738e-9, (7, 7) = 0.2855121738093055e-9, (7, 8) = -0.675308191598574e-9, (7, 9) = 0.11515466169445138e-8, (7, 10) = 0.8381176155292086e-9, (8, 1) = 0.861282175498395e-10, (8, 2) = 0.7455834471066683e-10, (8, 3) = -0.17419550139864895e-10, (8, 4) = 0.30987130932945824e-10, (8, 5) = -0.7320192655697801e-10, (8, 6) = 0.18515249893568048e-9, (8, 7) = 0.11596105360612101e-9, (8, 8) = -0.2784547335215155e-9, (8, 9) = 0.12910052205530779e-8, (8, 10) = 0.42953016229053193e-9, (9, 1) = 0.9918187742626932e-10, (9, 2) = 0.38862666834123524e-10, (9, 3) = -0.1089617534806676e-10, (9, 4) = 0.16730496947829825e-10, (9, 5) = -0.3978809508672104e-10, (9, 6) = 0.9984546072640248e-10, (9, 7) = 0.1708415060360776e-10, (9, 8) = -0.4544627550603776e-10, (9, 9) = 0.13917730547227234e-8, (9, 10) = 0.31641777503621664e-10, (10, 1) = 0.10904704786999959e-9, (10, 2) = 0.5781133598196827e-11, (10, 3) = -0.502288406772731e-11, (10, 4) = 0.33510840323527255e-11, (10, 5) = -0.7790092837651061e-11, (10, 6) = 0.2170526429654813e-10, (10, 7) = -0.21355469385880657e-10, (10, 8) = 0.4621401728688786e-10, (10, 9) = 0.14033732203404067e-8, (10, 10) = -0.23302982297714467e-9, (11, 1) = 0.11162627244860777e-9, (11, 2) = -0.17479544399985724e-10, (11, 3) = -0.23031272075957808e-11, (11, 4) = -0.27313437955063483e-11, (11, 5) = 0.7003418680788191e-11, (11, 6) = -0.14469885483035401e-10, (11, 7) = -0.27063191299430252e-10, (11, 8) = 0.6095459709954987e-10, (11, 9) = 0.13423215541803345e-8, (11, 10) = -0.3725164350319915e-9, (12, 1) = 0.10780168124769583e-9, (12, 2) = -0.3125189903400005e-10, (12, 3) = -0.1753591718781003e-11, (12, 4) = -0.3690710538137821e-11, (12, 5) = 0.961685900055666e-11, (12, 6) = -0.2142310131258488e-10, (12, 7) = -0.20644156937819316e-10, (12, 8) = 0.4692927104229764e-10, (12, 9) = 0.12377905788335966e-8, (12, 10) = -0.42471859556525036e-9, (13, 1) = 0.99646598645501e-10, (13, 2) = -0.377258444099372e-10, (13, 3) = -0.2070056599185993e-11, (13, 4) = -0.2570132689108194e-11, (13, 5) = 0.7211745460694847e-11, (13, 6) = -0.16300431684961348e-10, (13, 7) = -0.12512335996769459e-10, (13, 8) = 0.28554757799377127e-10, (13, 9) = 0.1113910018070198e-8, (13, 10) = -0.4244794702671659e-9, (14, 1) = 0.8912683940245015e-10, (14, 2) = -0.3918729272293496e-10, (14, 3) = -0.2495072900665989e-11, (14, 4) = -0.1162024798732049e-11, (14, 5) = 0.4014835030614173e-11, (14, 6) = -0.9169972855827749e-11, (14, 7) = -0.63341094596894245e-11, (14, 8) = 0.14491700772464273e-10, (14, 9) = 0.9866598583275541e-9, (14, 10) = -0.3966017779451776e-9, (15, 1) = 0.7774599692584211e-10, (15, 2) = -0.3752686756359315e-10, (15, 3) = -0.27535813033481937e-11, (15, 4) = -0.13560651271413173e-12, (15, 5) = 0.16038468209776116e-11, (15, 6) = -0.3849007127365619e-11, (15, 7) = -0.25783927128797387e-11, (15, 8) = 0.5919105934559633e-11, (15, 9) = 0.8652153753661252e-9, (15, 10) = -0.3567812365329655e-9, (16, 1) = 0.6652049768254916e-10, (16, 2) = -0.3414966656361681e-10, (16, 3) = -0.281988452855858e-11, (16, 4) = 0.4230435236426798e-12, (16, 5) = 0.17398882343683627e-12, (16, 6) = -0.9122380991466562e-12, (16, 7) = -0.6455818337628753e-12, (16, 8) = 0.15010410498291804e-11, (16, 9) = 0.7540451086669297e-9, (16, 10) = -0.3141387427205294e-9, (17, 1) = 0.5606173774967659e-10, (17, 2) = -0.30020961225253956e-10, (17, 3) = -0.27518534592488496e-11, (17, 4) = 0.6296740855041813e-12, (17, 5) = -0.5547294467981278e-12, (17, 6) = 0.20270527160917344e-12, (17, 7) = 0.18064736026356642e-12, (17, 8) = -0.3905172216891986e-12, (17, 9) = 0.6546909867233166e-9, (17, 10) = -0.27351503125792653e-9, (18, 1) = 0.46682140236185735e-10, (18, 2) = -0.25756635055967486e-10, (18, 3) = -0.26086852132542796e-11, (18, 4) = 0.6302711397705355e-12, (18, 5) = -0.8878537939351472e-12, (18, 6) = 0.24128768220298123e-12, (18, 7) = 0.43189091916683493e-12, (18, 8) = -0.968518876279622e-12, (18, 9) = 0.5670343628056239e-9, (18, 10) = -0.2371544337592204e-9, (19, 1) = 0.3849127021837058e-10, (19, 2) = -0.2171770586601584e-10, (19, 3) = -0.2415272035522141e-11, (19, 4) = 0.5689767982310255e-12, (19, 5) = -0.9620580482767798e-12, (19, 6) = -0.659644939262808e-13, (19, 7) = 0.42941550244357153e-12, (19, 8) = -0.9666929553604865e-12, (19, 9) = 0.4901117781718798e-9, (19, 10) = -0.20582228492958968e-9, (20, 1) = 0.314717476569805e-10, (20, 2) = -0.18091309528513952e-10, (20, 3) = -0.2136247120882874e-11, (20, 4) = 0.6379454533661625e-12, (20, 5) = -0.6161098837488019e-12, (20, 6) = 0.23416083329642884e-12, (20, 7) = 0.34101694377417256e-12, (20, 8) = -0.7682235925193444e-12, (20, 9) = 0.42260387276361414e-9, (20, 10) = -0.179497731032558e-9, (21, 1) = 0.25533635506275825e-10, (21, 2) = -0.14952771195169557e-10, (21, 3) = -0.16416832994500804e-11, (21, 4) = 0.11791529247580888e-11, (21, 5) = 0.7798544960309523e-12, (21, 6) = 0.2823741041069092e-11, (21, 7) = 0.2423419281614204e-12, (21, 8) = -0.5457764380638867e-12, (21, 9) = 0.36310938131458793e-9, (21, 10) = -0.15778039276120044e-9, (22, 1) = 0.2055136528254856e-10, (22, 2) = -0.12310100686569972e-10, (22, 3) = -0.6701381783305104e-12, (22, 4) = 0.27917887297545322e-11, (22, 5) = 0.45073815608650915e-11, (22, 6) = 0.10659675641184047e-10, (22, 7) = 0.1608025564261306e-12, (22, 8) = -0.3619010283961612e-12, (22, 9) = 0.3102856588896498e-9, (22, 10) = -0.1401182464414312e-9, (23, 1) = 0.16387131522839006e-10, (23, 2) = -0.10134058522368358e-10, (23, 3) = 0.11379034069672152e-11, (23, 4) = 0.62764336923731074e-11, (23, 5) = 0.12339581500029782e-10, (23, 6) = 0.27725954147974806e-10, (23, 7) = 0.10173926753325276e-12, (23, 8) = -0.22882162562999816e-12, (23, 9) = 0.26290412444406635e-9, (23, 10) = -0.12594178597286723e-9, (24, 1) = 0.1290453948623096e-10, (24, 2) = -0.837794723148123e-11, (24, 3) = 0.3905562816707579e-11, (24, 4) = 0.11900344754293836e-10, (24, 5) = 0.24885851691514555e-10, (24, 6) = 0.55422993887015675e-10, (24, 7) = 0.6211606739019313e-13, (24, 8) = -0.13970223821872075e-12, (24, 9) = 0.2198333085316357e-9, (24, 10) = -0.11479370380103057e-9, (25, 1) = 0.997536078810206e-11, (25, 2) = -0.6991146102083573e-11, (25, 3) = 0.63507533316961455e-11, (25, 4) = 0.16791139891499582e-10, (25, 5) = 0.35762196075988775e-10, (25, 6) = 0.7959540572191625e-10, (25, 7) = 0.36850969059663587e-13, (25, 8) = -0.8308155446801263e-13, (25, 9) = 0.17992714737915042e-9, (25, 10) = -0.1065877465186346e-9, (26, 1) = 0.7480871818945516e-11, (26, 2) = -0.5930208513432184e-11, (26, 3) = 0.3010948031507825e-11, (26, 4) = 0.8724207171909238e-11, (26, 5) = 0.17664364436851125e-10, (26, 6) = 0.3933208726169353e-10, (26, 7) = 0.2129475188648912e-13, (26, 8) = -0.485258513966945e-13, (26, 9) = 0.14177855576602702e-9, (26, 10) = -0.10215808691815177e-9, (27, 1) = 0.53088036096513784e-11, (27, 2) = -0.5169847594237262e-11, (27, 3) = -0.19489062135178172e-10, (27, 4) = -0.422512467393557e-10, (27, 5) = -0.964830020285085e-10, (27, 6) = -0.21555908586422648e-9, (27, 7) = 0.11913032652489058e-13, (27, 8) = -0.28204435558645146e-13, (27, 9) = 0.10352686247853766e-9, (27, 10) = -0.10378676540291118e-9, (28, 1) = 0.33520098641160794e-11, (28, 2) = -0.47032338345481124e-11, (28, 3) = -0.7618919909389643e-10, (28, 4) = -0.16977375183076047e-9, (28, 5) = -0.38213439007653123e-9, (28, 6) = -0.8546708466493403e-9, (28, 7) = 0.6242859695004346e-14, (28, 8) = -0.16842245656436337e-13, (28, 9) = 0.6421297846880997e-10, (28, 10) = -0.11233042434166181e-9, (29, 1) = 0.15488081008834392e-11, (29, 2) = -0.445313247306337e-11, (29, 3) = -0.11362033533673472e-9, (29, 4) = -0.25369627867564546e-9, (29, 5) = -0.569701039696018e-9, (29, 6) = -0.1273870847433359e-8, (29, 7) = 0.2625216688229959e-14, (29, 8) = -0.11204968834806214e-13, (29, 9) = 0.3014365196461356e-10, (29, 10) = -0.11119540976537309e-9, (30, 1) = .0, (30, 2) = -0.4286795926022271e-11, (30, 3) = .0, (30, 4) = .0, (30, 5) = -0.1819568429845308e-11, (30, 6) = -0.19476371241333025e-11, (30, 7) = .0, (30, 8) = -0.9575568470342801e-14, (30, 9) = .0, (30, 10) = -0.9728157970357238e-10}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [10, 30, [chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(10, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(10, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(30, 10, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = yout[i], i = 1 .. 10)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[30] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(4.895400347360599e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [10, 30, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[30] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[30] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(10, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0.}); `dsolve/numeric/hermite`(30, 10, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 10)] end proc, (2) = Array(0..0, {}), (3) = [eta, chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[chi(eta), diff(chi(eta), eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), diff(diff(diff(f(eta), eta), eta), eta), g(eta), diff(g(eta), eta), theta(eta), diff(theta(eta), eta)]'[i] = res[i+1], i = 1 .. 10)] catch: error end try end proc

 (4)
> 

plots:-odeplot( sol,
                [ [eta, theta(eta)],
                  [eta, g(eta)],
                  [eta, f(eta)],
                  [eta, chi(eta)]
                ],
                eta=0..10,
                color=[red, green, blue, black]
              );

 
> 

 

 

 
> 

 

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