Re: NDSolve with NIntegrate for a PDE where the unknown function is integrated wrt its variables
- To: mathgroup at smc.vnet.net
- Subject: [mg119091] Re: NDSolve with NIntegrate for a PDE where the unknown function is integrated wrt its variables
- From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
- Date: Sat, 21 May 2011 06:50:16 -0400 (EDT)
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