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Question: unevaluated integral

Question:unevaluated integral

J4James 355 Maple
ode dsolve numeric differential-equations bvp
December 02 2020
1


 

[Preliminary analysis of the Question by Carl Love:

 

In the worksheet below, the OP numerically solves a BVP on an interval a..b, for several values of a parameter. Using the numeric solution procedures returned by dsolve, he wants to numerically integrate an algebraic expression (named P1 below) that uses several of the BVP's dependent variables as well as its independent variable. This integral is to be done on an interval c..d, where a < c < d < b (all inequalities strict). He's having trouble coming up with the correct syntax for this.

 

I (Carl) am confident that the dsolve calls are all syntactically correct and that they return solution procedures in the usual manner without raising any issues, numerical or otherwise. Whether the integrations will ultimately require some adjustments to dsolve's error-control options, I don't know at this point. This Question is only about syntax required to perform the integrations. Any error-control adjustments, if they're needed at all, will be handled later.

 

I (Carl) have only edited the the OP's worksheet to remove a large amount of content that is irrelevant to Answering this Question. I haven't changed any of the content; I've only deleted. Of course, I already have several ideas about what needs to be done, but up until this point I haven't acted as an Answerer but rather as a Moderator and Editor making this Question suitable for posting.

 

--Carl Love]

> 

restart;
> 

 

> 

eq1:=diff(f(y), y$4)+Uhs*diff(E(y),y$3)-(diff(f(y), y$2))+(diff(theta(y), y$1))= 0:
> 

eq2:=diff(theta(y), y$2)+(diff(f(y), y$2)+1)^2+1+diff(theta(y),y$2) = 0:
> 

E:=y->zeta*(cosh(k/2*(h1+h2-2*y)))/(cosh(k/2*(h1-h2))):
> 

bcs:=f(h1) = -(1/2)*(Q-1-d), f(h2) = (1/2)*(Q-1-d), (D(f))(h1) = -1, (D(f))(h2) = -1,theta(h1) = 0, theta(h2) = 1:
> 

 

> 

epsilon1:=0.1:d:=1:omega:=Pi/6:h1:=-(1+epsilon1*sin(2*Pi*x)):h2:=d+epsilon2*sin(2*Pi*x+omega):F:= Q-1-d:epsilon2:=0.5:x:=1:
> 

alpha:=Pi/6:
> 

de:=eq1,eq2,bcs:
> 

d1 := subs(Uhs =-2, zeta=3,k=1,[de]):
> 

param:= {Uhs =-2, zeta=3,k=1}:
> 

P1:= eval(diff(f(y), y$3)+Uhs*diff(E(y),y$2)-(diff(f(y), y$1)+1)+(theta(y))+sin(alpha),param);

diff(diff(diff(f(y), y), y), y)-3.524364340*cosh(-.1250000000+y)-(diff(f(y), y))-1/2+theta(y)

 (1)
> 

ec:=0.5:
> 

 

> 

for Q from -3 to 3 by ec do
F2[Q]:=dsolve(d1, numeric,maxmesh=25500,continuation=lambda1,output=listprocedure):
P2[Q]:=subs(F2[Q],P1):  
end do:
> 

for Q from -3 to 3 by ec do
P3[Q]:=evalf(Int(P2[Q],0..1));   
end do:

[Examination of any of the P2[Q] or P3[Q] will highlight the syntactic problem. --Carl]:

> 

P2[-3];

proc (y) local res, data, solnproc, `diff(diff(diff(f(y),y),y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0)) ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (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(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(diff(diff(f(y),y),y),y)` := pointto(data[2][5]); return ('`diff(diff(diff(f(y),y),y),y)`')(y) end if end if; try res := solnproc(outpoint); res[5] catch: error end try end proc-3.524364340*cosh(-.1250000000+proc (y) 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0)) ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); _solnproc := _dat[1]; if member(y, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(y, `=`) and member(lhs(y), ["initial", 'initial']) then if type(rhs(y), 'list') then _res := _solnproc("initial" = [0, op(rhs(y))]) else _res := _solnproc("initial" = [1, rhs(y)]) end if; if type(_res, 'list') then return _res[1] end if elif y = "sysvars" then return _dat[3] end if; y end proc)-proc (y) local res, data, solnproc, `diff(f(y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0)) ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (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(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(f(y),y)` := pointto(data[2][3]); return ('`diff(f(y),y)`')(y) end if end if; try res := solnproc(outpoint); res[3] catch: error end try end proc-1/2+proc (y) local res, data, solnproc, `theta(y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0)) ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (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(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `theta(y)` := pointto(data[2][6]); return ('`theta(y)`')(y) end if end if; try res := solnproc(outpoint); res[6] catch: error end try end proc

 (2)
> 

P3[-3];

Int(proc (y) local res, data, solnproc, `diff(diff(diff(f(y),y),y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0)) ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (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(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(diff(diff(f(y),y),y),y)` := pointto(data[2][5]); return ('`diff(diff(diff(f(y),y),y),y)`')(y) end if end if; try res := solnproc(outpoint); res[5] catch: error end try end proc-3.524364340*cosh(-.1250000000+proc (y) 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0)) ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); _solnproc := _dat[1]; if member(y, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(y, `=`) and member(lhs(y), ["initial", 'initial']) then if type(rhs(y), 'list') then _res := _solnproc("initial" = [0, op(rhs(y))]) else _res := _solnproc("initial" = [1, rhs(y)]) end if; if type(_res, 'list') then return _res[1] end if elif y = "sysvars" then return _dat[3] end if; y end proc)-1.*proc (y) local res, data, solnproc, `diff(f(y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0)) ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (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(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(f(y),y)` := pointto(data[2][3]); return ('`diff(f(y),y)`')(y) end if end if; try res := solnproc(outpoint); res[3] catch: error end try end proc-.5000000000+proc (y) local res, data, solnproc, `theta(y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 6)] 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0)) ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (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(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `theta(y)` := pointto(data[2][6]); return ('`theta(y)`')(y) end if end if; try res := solnproc(outpoint); res[6] catch: error end try end proc, 0. .. 1.)

 (3)
> 

 

``

Note: If I remove the cosh from P1 then everything works fine.

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