tomleslie

13766 Reputation

19 Badges

14 years, 12 days

MaplePrimes Activity


These are answers submitted by tomleslie

because it is a matrix with 702 entries. The attached will display the first 10 or so - al the others are accessible. If you really wan to display all 702 entries, then insert interface(rtablesize=[702,4])

restart

eqn := diff(f(x), `$`(x, 3))+f(x)*(diff(f(x), `$`(x, 2)))-(diff(f(x), x))*(diff(f(x), x)-lambda) = 0

diff(diff(diff(f(x), x), x), x)+f(x)*(diff(diff(f(x), x), x))-(diff(f(x), x))*(diff(f(x), x)-lambda) = 0

(1)

bcs := f(0) = 0, (D(f))(0) = 1, (D(f))(a) = 0

f(0) = 0, (D(f))(0) = 1, (D(f))(a) = 0

(2)

params := [lambda = 0, a = 7]

[lambda = 0, a = 7]

(3)

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

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(15, {(1) = .0, (2) = .45884128660916607, (3) = .9251421721231284, (4) = 1.401244238977895, (5) = 1.891536505380774, (6) = 2.3948746631301048, (7) = 2.906535879536887, (8) = 3.4244168392907524, (9) = 3.944232981227012, (10) = 4.465274846431488, (11) = 4.9866275238674245, (12) = 5.508155422287264, (13) = 6.0296538384388905, (14) = 6.530766339216415, (15) = 7.0}, datatype = float[8], order = C_order); Y := Matrix(15, 3, {(1, 1) = .0, (1, 2) = 1.0, (1, 3) = -1.000172555152507, (2, 1) = .3679661670444895, (2, 2) = .6319340558265536, (2, 3) = -.6322009415220234, (3, 1) = .6034477479501392, (3, 2) = .39630180329423215, (3, 3) = -.3966825839137023, (4, 1) = .753525816927324, (4, 2) = .24601437619234381, (4, 3) = -.24651188973274546, (5, 1) = .8488142381644157, (5, 2) = .15045494206630705, (5, 3) = -.15106012272466318, (6, 1) = .9082488893736861, (6, 2) = 0.9069190108816673e-1, (6, 3) = -0.9138807321047741e-1, (7, 1) = .9444907528720965, (7, 2) = 0.5407468844222717e-1, (7, 3) = -0.5484229949404112e-1, (8, 1) = .9662592046414542, (8, 2) = 0.3189417483562893e-1, (8, 3) = -0.3271500187083119e-1, (9, 1) = .9790925647282462, (9, 2) = 0.18623696527793335e-1, (9, 3) = -0.19482428019138014e-1, (10, 1) = .986555766088315, (10, 2) = 0.10705793334502571e-1, (10, 3) = -0.1159074703199189e-1, (11, 1) = .9908027381592555, (11, 2) = 0.5992523847149354e-2, (11, 3) = -0.6895179787550211e-2, (12, 1) = .9931335723717829, (12, 2) = 0.31876605099718258e-2, (12, 3) = -0.41020283287439415e-2, (13, 1) = .9943233338103351, (13, 2) = 0.1518931255261683e-2, (13, 3) = -0.2440894633976018e-2, (14, 1) = .9948231976119695, (14, 2) = 0.555802515946153e-3, (14, 3) = -0.148243657690736e-2, (15, 1) = .9949434885398212, (15, 2) = .0, (15, 3) = -0.9294255132965231e-3}, datatype = float[8], order = C_order); YP := Matrix(15, 3, {(1, 1) = 1.0, (1, 2) = -1.000172555152507, (1, 3) = 1.0, (2, 1) = .6319340558265536, (2, 2) = -.6322009415220234, (2, 3) = .6319692081671742, (3, 1) = .39630180329423215, (3, 2) = -.3966825839137023, (3, 3) = .39643233120802607, (4, 1) = .24601437619234381, (4, 2) = -.24651188973274546, (4, 3) = .2462761463864735, (5, 1) = .15045494206630705, (5, 2) = -.15106012272466318, (5, 3) = .15085867257973395, (6, 1) = 0.9069190108816673e-1, (6, 2) = -0.9138807321047741e-1, (6, 3) = 0.9122813691840304e-1, (7, 1) = 0.5407468844222717e-1, (7, 2) = -0.5484229949404112e-1, (7, 3) = 0.5472211666848783e-1, (8, 1) = 0.3189417483562893e-1, (8, 2) = -0.3271500187083119e-1, (8, 3) = 0.32628410075998704e-1, (9, 1) = 0.18623696527793335e-1, (9, 2) = -0.19482428019138014e-1, (9, 3) = 0.19421942488750624e-1, (10, 1) = 0.10705793334502571e-1, (10, 2) = -0.1159074703199189e-1, (10, 3) = 0.11549532328603701e-1, (11, 1) = 0.5992523847149354e-2, (11, 2) = -0.6895179787550211e-2, (11, 3) = 0.6867673355663757e-2, (12, 1) = 0.31876605099718258e-2, (12, 2) = -0.41020283287439415e-2, (12, 3) = 0.4084023227622559e-2, (13, 1) = 0.1518931255261683e-2, (13, 2) = -0.2440894633976018e-2, (13, 3) = 0.24293456420930028e-2, (14, 1) = 0.555802515946153e-3, (14, 2) = -0.148243657690736e-2, (14, 3) = 0.14750712121326542e-2, (15, 1) = .0, (15, 2) = -0.9294255132965231e-3, (15, 3) = 0.9247258625371567e-3}, 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(15, {(1) = .0, (2) = .45884128660916607, (3) = .9251421721231284, (4) = 1.401244238977895, (5) = 1.891536505380774, (6) = 2.3948746631301048, (7) = 2.906535879536887, (8) = 3.4244168392907524, (9) = 3.944232981227012, (10) = 4.465274846431488, (11) = 4.9866275238674245, (12) = 5.508155422287264, (13) = 6.0296538384388905, (14) = 6.530766339216415, (15) = 7.0}, datatype = float[8], order = C_order); Y := Matrix(15, 3, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.9846501960989505e-10, (2, 1) = -0.14082608794708346e-6, (2, 2) = 0.1411835385771021e-6, (2, 3) = -0.14048601936730212e-6, (3, 1) = -0.14176889024724998e-6, (3, 2) = 0.14281355817553083e-6, (3, 3) = -0.14151890228908607e-6, (4, 1) = -0.10012730732250013e-6, (4, 2) = 0.10205544289443828e-6, (4, 3) = -0.10034339447818287e-6, (5, 1) = -0.55853751163662226e-7, (5, 2) = 0.5875209754413099e-7, (5, 3) = -0.5683132046670593e-7, (6, 1) = -0.21235331674583595e-7, (6, 2) = 0.25101208483958363e-7, (6, 3) = -0.23147969488423017e-7, (7, 1) = 0.9925593820904865e-9, (7, 2) = 0.3779595840388026e-8, (7, 3) = -0.19127586900557814e-8, (8, 1) = 0.12392595524747908e-7, (8, 2) = -0.6799322977513806e-8, (8, 3) = 0.8511315622508796e-8, (9, 1) = 0.1640238741867568e-7, (9, 2) = -0.100822144674156e-7, (9, 3) = 0.1161080201767941e-7, (10, 1) = 0.16349770708917644e-7, (10, 2) = -0.939164853989075e-8, (10, 3) = 0.10733390184191948e-7, (11, 1) = 0.14624569857460525e-7, (11, 2) = -0.7108454519144011e-8, (11, 3) = 0.8276116737352355e-8, (12, 1) = 0.12605317572479922e-7, (12, 2) = -0.45996593262353215e-8, (12, 3) = 0.5614895108421162e-8, (13, 1) = 0.10923893492661616e-7, (13, 2) = -0.24852987200001826e-8, (13, 3) = 0.3373601787064303e-8, (14, 1) = 0.9770889428210786e-8, (14, 2) = -0.9563326962688922e-9, (14, 3) = 0.17467581538982356e-8, (15, 1) = 0.9139737170738694e-8, (15, 2) = .0, (15, 3) = 0.7189132222848026e-9}, 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[15] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.4281355817553083e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [3, 15, [f(x), diff(f(x), x), diff(diff(f(x), x), x)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[15] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[15] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(3, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(15, 3, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(3, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(15, 3, X, Y, outpoint, yout, L, V) end if; [x = outpoint, seq('[f(x), diff(f(x), x), diff(diff(f(x), x), x)]'[i] = yout[i], i = 1 .. 3)] 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[15] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.4281355817553083e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [3, 15, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[15] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[15] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(15, 3, 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(3, {(1) = 0., (2) = 0., (3) = 0.}); `dsolve/numeric/hermite`(15, 3, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 3)] end proc, (2) = Array(0..0, {}), (3) = [x, f(x), diff(f(x), x), diff(diff(f(x), x), x)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [x = res[1], seq('[f(x), diff(f(x), x), diff(diff(f(x), x), x)]'[i] = res[i+1], i = 1 .. 3)] catch: error  end try end proc

(4)

NULL

Matrix([ lhs~(sol(0)),
         seq(rhs~(sol(j)), j=0..7, 0.01)
       ]
      );

_rtable[36893488148684478692]

(5)

 

Download matres.mw

  1. The dsolve() command accepts a "flat" list/set of equations and initial/boundary conditions - you have a set of three lists. This is a simple syntax error which can be corrected by writing dsolve({diffeqs[], initial_values[], final_conditions[]}, numeric, output = listprocedure);
  2. Your system contains three first-order ODES, which means you can only have a grand total of three boundary/initial conditions. You have five (maybe 6, see next point)
  3. You cannot have an inequality as a meaningful boundary condition,  so 0 < B(5.0) is completely unacceptable
  4. Your system cannot include an entirely arbitrary function 'w(t)', with no derivatives or boundary/initial conditions

as in the "toy" example attached.

  restart;
  with(plots):
  with(plottools):

  p1:=cylinder([0,0,0], 1, Pi, transparency=0.5, color=blue):
  p2:=spacecurve([cos(2*t),sin(2*t),t],t=0..Pi, color=red, thickness=5):
  display([p1,p2]);
   

 

 

Download combPlot.mw

is that in the defintion of the function 'f', you have used both curly braces (ie {}) and square braces (ie []) for the simple grouping of terms. In Maple anything within {} designates a set and anythin within [] designates a member of an indexable quantity. For simple grouping of terms, use () only

depending on the precise nature of the file to be imported. The attached worksheet will read a file containing

[[0.1, 0.0769540597, 0.1477783335, 0.1393069312, 

  0.0763361154, 0.1477867626, 0.1393072151, 0.0763361266, 

  0.1477867830, 0.1393071934], [0.3, 0.1093424148, 0.1120401102, 

  0.1509302274, 0.1072278404, 0.1121142033, 0.1509369166, 

  0.1072278479, 0.1121142168, 0.1509369024], [0.5, 0.1392030568, 

  0.0853083077, 0.1558066181, 0.1353291378, 0.0855066806, 

  0.1558355785, 0.1353291558, 0.08550671332, 0.1558355439], [0.7, 

  0.1662374563, 0.0652194693, 0.1562235596, 0.1604342222, 

  0.0655908735, 0.1562974878, 0.1604342352, 0.06559089617, 

  0.1562974637], [0.9, 0.1903821623, 0.0500537619, 0.1537887672, 

  0.1825594352, 0.0506356391, 0.1539346707, 0.1825594528, 

  0.05063567192, 0.1539346352], [1.1, 0.2117168860, 0.0385555127, 

  0.1496220815, 0.2018541863, 0.0393727175, 0.1498707561, 

  0.2018542024, 0.03937274753, 0.1498707234], [1.3, 0.2303874000, 

  0.0298096396, 0.1444864012, 0.2185409755, 0.0308687065, 

  0.1448804021, 0.2185409880, 0.03086872986, 0.1448803765], [1.5, 

  0.2465077820, 0.0231661161, 0.1388614678, 0.2328759081, 

  0.0244336214, 0.1394893808, 0.2328759200, 0.02443364533, 

  0.1394893543]]

and produce a matrix. You will have to change the 'pathname' and 'fileName' assignments to something appropriate for your installation.

  restart;
  pathName:="C:/Users/TomLeslie/Desktop/":
  fileName:="dat.txt":
  Data:=readline(StringTools:-Join( [pathName, fileName],"")):
  line:=1:
  while line<>0 do
        line:=readline(StringTools:-Join( [pathName, fileName],"")):
        if   `and`(length(line)>0, line<>0)
        then Data:=StringTools:-Join( [Data, line]);
        fi;
  od:
  myData:=Matrix(parse~(Data));

Matrix(8, 10, {(1, 1) = .1, (1, 2) = 0.769540597e-1, (1, 3) = .1477783335, (1, 4) = .1393069312, (1, 5) = 0.763361154e-1, (1, 6) = .1477867626, (1, 7) = .1393072151, (1, 8) = 0.763361266e-1, (1, 9) = .1477867830, (1, 10) = .1393071934, (2, 1) = .3, (2, 2) = .1093424148, (2, 3) = .1120401102, (2, 4) = .1509302274, (2, 5) = .1072278404, (2, 6) = .1121142033, (2, 7) = .1509369166, (2, 8) = .1072278479, (2, 9) = .1121142168, (2, 10) = .1509369024, (3, 1) = .5, (3, 2) = .1392030568, (3, 3) = 0.853083077e-1, (3, 4) = .1558066181, (3, 5) = .1353291378, (3, 6) = 0.855066806e-1, (3, 7) = .1558355785, (3, 8) = .1353291558, (3, 9) = 0.8550671332e-1, (3, 10) = .1558355439, (4, 1) = .7, (4, 2) = .1662374563, (4, 3) = 0.652194693e-1, (4, 4) = .1562235596, (4, 5) = .1604342222, (4, 6) = 0.655908735e-1, (4, 7) = .1562974878, (4, 8) = .1604342352, (4, 9) = 0.6559089617e-1, (4, 10) = .1562974637, (5, 1) = .9, (5, 2) = .1903821623, (5, 3) = 0.500537619e-1, (5, 4) = .1537887672, (5, 5) = .1825594352, (5, 6) = 0.506356391e-1, (5, 7) = .1539346707, (5, 8) = .1825594528, (5, 9) = 0.5063567192e-1, (5, 10) = .1539346352, (6, 1) = 1.1, (6, 2) = .2117168860, (6, 3) = 0.385555127e-1, (6, 4) = .1496220815, (6, 5) = .2018541863, (6, 6) = 0.393727175e-1, (6, 7) = .1498707561, (6, 8) = .2018542024, (6, 9) = 0.3937274753e-1, (6, 10) = .1498707234, (7, 1) = 1.3, (7, 2) = .2303874000, (7, 3) = 0.298096396e-1, (7, 4) = .1444864012, (7, 5) = .2185409755, (7, 6) = 0.308687065e-1, (7, 7) = .1448804021, (7, 8) = .2185409880, (7, 9) = 0.3086872986e-1, (7, 10) = .1448803765, (8, 1) = 1.5, (8, 2) = .2465077820, (8, 3) = 0.231661161e-1, (8, 4) = .1388614678, (8, 5) = .2328759081, (8, 6) = 0.244336214e-1, (8, 7) = .1394893808, (8, 8) = .2328759200, (8, 9) = 0.2443364533e-1, (8, 10) = .1394893543})

(1)

 

 

Download readDat.mw

 

 

  1. Your pdes use the parameter 'phi', which is nowhere assigned a value, although the list of parameters contains two values for the parameter 'delta'. Maybe one of these is supposed to be a phi-value?
  2. The parameter list has two values for 'nu'. Which ine do you want to use?
  3. The supplied graphs are two-dimensional. Any graph of u(y,t) versus 'y' and 't' is obviously three-dimensional. Hence the 2D graphs you supply represent a "slice" through the 3D graph at a specific value of 't',. This value is nowhere given

When you resolve the above problema, the code you need will be something like that shown in the attached, where I have guessed that delta=0.1, phi=0.5, nu=1 and plotted u(y, 2). (Obviously these guesses may well be completely wrong!). The attached only supplies a graph for the variation of the parameter 'Pr'. Variation with respect to other parametrs would be performed similarly.

  restart;
  inf:=10:
  pdes:= diff(u(y,t),t)-xi*diff(u(y,t),y)=diff(u(y,t),y$2)/(1+lambda__t)+Gr*theta(y,t)+Gc*C(y,t)-M*u(y,t)-K*u(y,t),
         diff(theta(y,t),t)-xi*diff(theta(y,t),y)=1/Pr*diff(theta(y,t),y$2)+phi*theta(y,t),
         diff(C(y,t),t)-xi*diff(C(y,t),y)=1/Sc*diff(C(y,t),y$2)-delta*C(y,t)+nu*theta(y,t):
  conds:= u(y,0)=0, theta(y,0)=0, C(y,0)=0,
          u(0,t)=0, D[1](theta)(0,t)=-1, D[1](C)(0,t)=-1,
          u(inf,t)=0, theta(inf,t)=0, C(inf,t)=0:
  pars:= { Gr=1, Gc=1, M=1, nu=1, lambda__t=0.5,
           Sc=0.78, delta=0.1, phi=0.5, K=0.5, xi=0.5
         }        

{Gc = 1, Gr = 1, K = .5, M = 1, Sc = .78, delta = .1, nu = 1, phi = .5, xi = .5, lambda__t = .5}

(1)

  PrVals:=[0.71, 1.00, 3.00, 7.00]:
  colors:=[red, green, blue, black]:
  for j from 1 to numelems(PrVals) do
      pars1:=`union`( pars, {Pr=PrVals[j]}):
      pdSol:= pdsolve( eval([pdes], pars1),
                       eval([conds], pars1),
                       numeric
                     );
      plt[j]:=pdSol:-plot( u(y,t), t=2, y=0..inf, numpoints=200, color=colors[j]);
  od:
  plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);

 

 

 

Download badPDE.mw

 

 your ode will not produce any numerical answers, because

  1. you use the name gamma in your ODEs, then define a parameter called localgamma - if these are supposed to be the same, then I suggesst using the latter name throughout
  2. you use the name ic4 in one of your initial conditions, then define a parameter called ics4 - if these are supposed to be the same, then be consistent
  3. the parameter N is used in your ODEs and is nowhere defined - it will have to be

In the attached, I have guessed your intent and fixed all of the above. It is up to you to determine whether my guesses are correct before further progress can be made.

restart;

with(plots):
with(plottools):
with(DEtools):

eqn1 := diff(V(t), t) = pi*p - (alpha + mu)*V(t),
        V(0) = ic1;

eqn2 := diff(S(t), t) = alpha*V(t) + (1 - p)*pi - beta*S(t)*In(t)/N - mu*S(t),
        S(0) = ic2;

eqn3 := diff(In(t), t) = beta*S(t)*In(t)/N - (mu + delta + localgamma)*In(t),
        In(0) = ic3;

eqn4 := diff(R(t), t) = localgamma*In(t) - mu*R(t),
        R(0) = ic4;

pi := 487845;
p := 0.948;
alpha := 0.054;
beta := 0.955;
mu := 0.005;
delta := 0.03;
localgamma := 0.935;
ic1 := 484465;
ic2 := 31999760;
ic3 := 26305;
ic4 := 12470;
N:=10000;
dsol := dsolve([eqn1, eqn2, eqn3, eqn4], numeric);

odeplot( dsol,
         [ [t, V(t), color = plum],
           [t, S(t), color = blue],
           [t, In(t), color = cyan],
           [t, R(t), color = green]
         ],
         t = 0 .. 200,
         thickness = 3
       );

diff(V(t), t) = pi*p-(alpha+mu)*V(t), V(0) = ic1

 

diff(S(t), t) = alpha*V(t)+(1-p)*pi-beta*S(t)*In(t)/N-mu*S(t), S(0) = ic2

 

diff(In(t), t) = beta*S(t)*In(t)/N-(mu+delta+localgamma)*In(t), In(0) = ic3

 

diff(R(t), t) = localgamma*In(t)-mu*R(t), R(0) = ic4

 

487845

 

.948

 

0.54e-1

 

.955

 

0.5e-2

 

0.3e-1

 

.935

 

484465

 

31999760

 

26305

 

12470

 

10000

 

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 28, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..65, {(1) = 4, (2) = 4, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0, (64) = -1, (65) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.16522639105675312e-4, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..4, {(1) = 26305.0, (2) = 12470.0, (3) = 0.3199976e8, (4) = 484465.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..4, {(1) = .1, (2) = .1, (3) = .1, (4) = .1}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0}, datatype = float[8], order = C_order), Array(1..4, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0}, datatype = integer[8]), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..4, {(1) = 26305.0, (2) = 12470.0, (3) = 0.3199976e8, (4) = 484465.0}, datatype = float[8], order = C_order), Array(1..4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8], order = C_order), Array(1..4, {(1) = 80361961.23940001, (2) = 24532.825000000004, (3) = -80495946.83940001, (4) = 433893.625}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = In(t), Y[2] = R(t), Y[3] = S(t), Y[4] = V(t)]`; YP[1] := 0.9550000000e-4*Y[3]*Y[1]-.970*Y[1]; YP[2] := .935*Y[1]-0.5e-2*Y[2]; YP[3] := 0.54e-1*Y[4]+25367.940-0.9550000000e-4*Y[3]*Y[1]-0.5e-2*Y[3]; YP[4] := 462477.060-0.59e-1*Y[4]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = In(t), Y[2] = R(t), Y[3] = S(t), Y[4] = V(t)]`; YP[1] := 0.9550000000e-4*Y[3]*Y[1]-.970*Y[1]; YP[2] := .935*Y[1]-0.5e-2*Y[2]; YP[3] := 0.54e-1*Y[4]+25367.940-0.9550000000e-4*Y[3]*Y[1]-0.5e-2*Y[3]; YP[4] := 462477.060-0.59e-1*Y[4]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 27 ) = (""), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0), ( 28 ) = (0)  ] ))  ] ); _y0 := Array(0..4, {(1) = 0., (2) = 26305., (3) = 12470., (4) = 31999760.}); _vmap := array( 1 .. 4, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if elif type(_xin, `=`) and lhs(_xin) = "setdatacallback" then if not type(rhs(_xin), 'nonegint') then error "data callback must be a nonnegative integer (address)" end if; _dtbl[1][28] := rhs(_xin) else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, In(t), R(t), S(t), V(t)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

 

 

 

Download odeProb.mw

Maple is producing two solutions, each of which is a two-element arctan() function, ie arctan(x,y).

Suggest arctan() help page for further enlightment

Your wotksheet executes without error in Maple2023, but produces errors in your version (Maple2018). I tried (briefly) to make it function in Maple2018, but I failed.
Best suggestion I can come up with is not to use units at all, then use the labels option of the plot() command, to produce axes labels - as in the attached.

restart; interface(version)

`Standard Worksheet Interface, Maple 2018.2, Windows 7, November 16 2018 Build ID 1362973`

(1)

v__0 := 60; theta := 45*Pi*(1/180); m := 1.0; b := 1; g := 9.81; v__x0 := v__0*cos(theta); v__y0 := v__0*sin(theta); v__x := v__0*cos(theta)*exp(-b*t/m); v__y := (m*g/b+v__y0)*exp(-b*t/m)-m*g/b; x := m*v__x0*(1-exp(-b*t/m))/b; y := (b*m*v__y0+g*m^2)*(1-exp(-b*t/m))/b^2-m*g*t/b

60

 

(1/4)*Pi

 

1.0

 

1

 

9.81

 

30*2^(1/2)

 

30*2^(1/2)

 

30*2^(1/2)*exp(-1.000000000*t)

 

(9.810+30*2^(1/2))*exp(-1.000000000*t)-9.810

 

30.0*2^(1/2)*(1-exp(-1.000000000*t))

 

(30.0*2^(1/2)+9.8100)*(1-exp(-1.000000000*t))-9.810*t

(2)

plot(x, t = 0 .. 4, labels = ['t(s)', 'x(m)']); plot(y, t = 0 .. 4, labels = ['t(s)', 'y(m)'])

 

 

test_function_X := unapply(x, t); test_function_Y := unapply(y, t); test := combine(evalf(test_function_X(4))); plot([x, y, t = 0 .. 4], labels = ['x(m)', 'y(m)']); plot([test_function_X(t), test_function_Y(t), t = 0 .. 4], labels = ['x(m)', 'y(m)'])

proc (t) options operator, arrow; 30.0*2^(1/2)*(1-exp(-1.000000000*t)) end proc

 

proc (t) options operator, arrow; (30.0*2^(1/2)+9.8100)*(1-exp(-1.000000000*t))-9.810*t end proc

 

41.64934011

 

 

 

``

Download noUnitsPlot.mw

 

provided that your expression is dimensionally correct. Nowhere in your original worksheeet did you specify that the variable 't' has 'seconds' as a unit. Even with this fix, the lost connection to kernel occurs in all versions of Maple up to Maple2022

See the  attached (in Maple2023 (which probably isn't very useful for you!)

restart; with(Units); theta := (40*Pi*(1/180))*Unit('rad'); v__0 := 1000*Unit('m')/Unit('s'); g := 9.81*Unit('m')/Unit('s')^2; y := v__0*t*Unit('s')*sin(theta)-(1/2)*g*(t*Unit('s'))^2; T := solve(y = 0, t); maximize(y)

Automatically loading the Units[Simple] subpackage
 

 

(2/9)*Pi*Units:-Unit(rad)

 

1000*Units:-Unit(m/s)

 

9.81*Units:-Unit(m/s^2)

 

(1000*t*sin((2/9)*Pi)-4.905000000*t^2)*Units:-Unit(m)

 

0., 131.0474230

 

21058.91494*Units:-Unit(m)

(1)

``

Download unitProb.mw

 

Everything "works" (ie all plots are produced)  in Maple 2023, except for

plot(f, t=0.9..1.12, adaptive=true);  #no graph

Either of the following "works" in Maple 2023

plot(f, t=0.9..1.12, adaptive=geometric);  #no graph
plot(f, t=0.9..1.12, adaptive=default);  #no graph

yould wrie your own numeric method, for a differential equation which has an analytic solution (unless you want it for comparison purposes). The attached has twow figures

  1. plot of your points
  2. plot of the analytic solution

restart

with(plots)

with(DEtools)

diff(y(x), x) = f(x, y(x))

diff(y(x), x) = f(x, y(x))

(1)

finite_diff_eq := (y[i+1]-y[i])/h = f(x[i], y[i])

(y[i+1]-y[i])/h = f(x[i], y[i])

(2)

y[i+1] := solve(finite_diff_eq, y[i+1])

f(x[i], y[i])*h+y[i]

(3)

h := 1; N := 10; x[0] := 0; y[0] := 1; f := proc (x, y) options operator, arrow; cos(x+y) end proc

1

 

10

 

0

 

1

 

proc (x, y) options operator, arrow; cos(x+y) end proc

(4)

for i from 0 to N do x[i+1] := x[i]+h; y[i+1] := evalf(y[i]+f(x[i], y[i]))*h end do; plot(convert(x, list), convert(y, list), style = pointline, symbol = solidcircle, symbolsize = 16, color = red)

 

restart; diff(y(x), x) = cos(x+y(x)); dsolve([%, y(0) = 1]); plot(rhs(%), x = 0 .. 10)

diff(y(x), x) = cos(x+y(x))

 

y(x) = -x+2*arctan(x+tan(1/2))

 

 

 

Download diffPlot.mw

 

you want the coeffiicients of a polynomial? As in the attached.

  restart;
  f:= n->expand( (3+2*x+3*x^2)^n );
#
# The polynomial
#
  f(7);
#
# Its coefficients
#
  coeffs( f(7), x);

proc (n) options operator, arrow; expand((3*x^2+2*x+3)^n) end proc

 

2187*x^14+10206*x^13+35721*x^12+83916*x^11+163107*x^10+249858*x^9+327369*x^8+352424*x^7+327369*x^6+249858*x^5+163107*x^4+83916*x^3+35721*x^2+10206*x+2187

 

2187, 10206, 35721, 83916, 163107, 249858, 327369, 352424, 327369, 249858, 163107, 83916, 35721, 10206, 2187

(1)

 

Download coeffs.mw

a bit more like the attached? (Arrays of plots do not render on this website - hence the download link only)

Download arrPlt.mw

extra "multiplication" symbol highlighted in the codesnnip below

eval(SensibilidadeK*(Profundidade, t, k, C), [k = 1, C = 1])
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