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Re: Numerical Solver for 2D/3D (Reaction-)Diffusion equation

On Tue, 4 Jan 2011, Alois wrote:

> I'm trying to solve numerically a 2d/3d reaction-diffusion equation
> using NDSolve. The system can be solved for one spatial dimension (+
> time dimension), but it does not converge for two spatial dimensions
> (x,y,t). Actually, I'm trying to use polar coordinates (r, phi, t),
> because the problem has a point source.
> I'm using NDsolve with the following method:
> Method -> {"MethodOfLines", "SpatialDiscretization" ->
> {"TensorProductGrid", "Coordinates" -> myGrid}
> which fails. Can you recommend a better method to solve the problem in
> 2D (and eventually in 3D) ?
> Kind regards,
>   Alois


things like

eqn = \[Rho]*cp*D[u[t, x, y], t] - \[Lambda]*
     D[u[t, x, y], x, x] + -\[Lambda]*D[u[t, x, y], y, y] ==
   f + r*u[t, x, y]*If[x == p1X, y == p1Y, 1, 0]

    bc, ic], u, {t, 0, tEnd}, {x, 0, xEnd}, {y, 0, yEnd},
   Method -> {"MethodOfLines",
     "SpatialDiscretization" -> {"TensorProductGrid",
        MaxPoints -> {35, 35}, MinPoints -> {35, 35}

work in principal. Now, the exact details depend on the equation 
parameters. Note that the Max and Min points need to be chosen 
such that the tensor grid generates a point {p1X,p1Y}.


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