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

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  Re: NDSolve with NIntegrate for a PDE where the unknown function is integrated wrt its variables ValeX <rjovale@gmail.com> - 2011-05-22 10:59 +0000

#2621 — Re: NDSolve with NIntegrate for a PDE where the unknown function is integrated wrt its variables

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.

thanks, but i dont think that this would work as one should call
instead of f[t, Yg[r, t], r] the expression with r1, f[t, Yg[r1, t],
r], which i dont think mathematica can interpret correctly

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