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Re: NDSolve with NIntegrate for a PDE where the unknown function is integrated wrt its variables

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On Fri, 20 May 2011, ValeX wrote:

> Hello, i know that this issue has been raised many times, but i cannot
> find an answer in the previous posts.
>
> I tried to reformulate my problem in a simple way:
>
> NDSolve[{Derivative[0, 1][Yg][r, t]==NIntegrate[A[r1] Yg[r1, t] , {r1,
> 1, r}] + B[r]/Yg[r, t], Yg[r, 0] == r}, {Yg}, {r, 1, 10}, {t, 0, 0.3}]
>
> where A and B are some functions, for example:
>
> A[r_] = r^-1; B[r_] = r + 10;
>
> Please help!
>
>


Perhaps like this

A[r_] = r^-1; B[r_] = r + 10;
ClearAll[f]
f[t_, y_, r_?NumberQ] := NIntegrate[A[r1] *y, {r1, 1, r}]

NDSolve[{
   Derivative[0, 1][Yg][r, t] == B[r]/Yg[r, t] + f[t, Yg[r, t], r],
   Yg[r, 0] == r,
   Yg[1, t] == 1,
   Yg[10, t] == 10
   }, Yg, {r, 1, 10}, {t, 0, 0.3}, SolveDelayed -> True]

You'd need to add the right boundary conditions.

Oliver

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Re: NDSolve with NIntegrate for a PDE where the unknown function is integrated wrt its variables Oliver Ruebenkoenig <ruebenko@wolfram.com> - 2011-05-21 10:50 +0000

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