Re: NDSolve with InterpolatingFunctions

• To: mathgroup at smc.vnet.net
• Subject: [mg8207] Re: [mg8114] NDSolve with InterpolatingFunctions
• From: seanross at worldnet.att.net
• Date: Mon, 18 Aug 1997 23:24:56 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Michael Bunk wrote:
>
> I would like to solve a partial differential equation containing an
> InterpolatingFunction object.
>
> The message from MATHEMATICA is:
>
>         Built-in routines cannot solve the partial differential equation
>
> Are there any packages to handle the problem?
>
> Michael Bunk
>
> Example:
>
>    \[Zeta]^2*Htilde[\[Xi]]^2*Derivative[1][Htilde][\[Xi]]*
>    Derivative[0, 1][\[CapitalTheta]][\[Xi], \[Zeta]] -
>    Derivative[0, 2][\[CapitalTheta]][\[Xi], \[Zeta]] +
>    \[Zeta]*Htilde[\[Xi]]^3*
>    Derivative[1, 0][\[CapitalTheta]][\[Xi], \[Zeta]] == 0
>
> with
>
>    Htilde\[Rule]InterpolatingFunction[{{0.,0.999999}},"<>"]
>
>
> --
> Michael Bunk
>
> Forschungszentrum Karlsruhe
> Institut fuer Angewandte Thermo- und Fluiddynamik
> Postfach 3640
> D-76021 Karlsruhe
> Tel.: 07247/82-2528

Have you considered writing your own PDE solver?  They aren't that hard,
especially with all the lovely array and list handling features of MMA.
Common methods would include:  Eulers, MidPoint and various orders of
Runga-Kutta.  Another option would be to use a fitted polynomial rather
than an interpolation function object.  You could even use the
interpolation function to generate a series of data points that you
would use to fit a polynomial to.

```

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