Compiled functions in NDSolve.

• To: mathgroup at smc.vnet.net
• Subject: [mg25642] Compiled functions in NDSolve.
• From: "Daniel Lisak" <xdl1 at poczta.onet.pl>
• Date: Wed, 18 Oct 2000 02:52:19 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```    Does anybody know how can I use compiled functions in NDSolve ?
I have some compiled functions (they all depend on 3 real
variables: t, ro, v):

potencjalX = Compile[{t, ro, v}, -176.276/(ro^2 + v^2 t^2)^3];
potencjalA = Compile[{t, ro, v}, -248.279/(ro^2 + v^2 t^2)^3];
potencjalB = Compile[{t, ro, v}, -319.691/(ro^2 + v^2 t^2)^3];
funfi = Compile[{t, ro, v}, ArcSin[ro/Sqrt[ro^2 + v^2t^2]]];
funF = Compile[{t, ro, v}, (potencjalB[t, ro, v] - potencjalA[t, ro, v])/2];
funv1 = Compile[{t, ro, v}, (potencjalA[t, ro, v] + potencjalB[t, ro,
v])/2];

and I want to solve ordinary differential equations:

rozw[apocz_, ro_, v_, tend_, nieskoncz_] := NDSolve[{
a1'[t] == a1[t] potencjalX[t, ro, v]/I,
a2'[t] == a2[t] potencjalB[t, ro, v]/I,
a3'[t] == a3[t] funv1[t, ro, v]/I +
a4[t] funF[t, ro, v] Exp[2I funfi[t, ro, v]]/I,
a4'[t] == a3[t] funF[t, ro, v] Exp[-2I funfi[t, ro, v]]/I +
a4[t] funv1[t, ro, v]/I,
a1[-nieskoncz] == apocz[[1]],
a2[-nieskoncz] == apocz[[2]],
a3[-nieskoncz] == apocz[[3]],
a4[-nieskoncz] == apocz[[4]]},
{a1, a2, a3, a4}, {t, -tend, tend}, MaxSteps -> 100000]

when I evaluate this function:

rozw[{0, 0, 1, 0}, 3, 0.0003, 75000., 75000.]

I see the following error:

CompiledFunction::cfsa: Argument t at position 1 should be a machine-size
real number.

Does anybody know how can I use these compiled functions in NDSolve ?

Daniel

```

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