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Re: NDSolve with 3 independent variables

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  • Subject: [mg122741] Re: NDSolve with 3 independent variables
  • From: Oliver Ruebenkoenig <ruebenko at>
  • Date: Tue, 8 Nov 2011 07:16:59 -0500 (EST)
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On Mon, 7 Nov 2011, iuval wrote:

> Trying to solve a pde with 3 independent variables using NDSolve.
> Getting the error message:
> NDSolve::ivone: Boundary values may only be specified for one
> independent variable. Initial values may only be specified at one
> value of the other independent variable.
> Does NDSolve work with 3 independent variables? I tried no boundary
> conditions and got the same message.


Yes it does.

L = 4;
ms = 20;(*ms=80*)
sol =
  NDSolve[{D[u[t, x, y, z], t, t] ==
     D[u[t, x, y, z], x, x] + D[u[t, x, y, z], y, y] +
      D[u[t, x, y, z], z, z] + Sin[u[t, x, y, z]],
    u[t, -L, y, z] == u[t, L, y, z], u[t, x, -L, z] == u[t, x, L, z],
    u[t, x, y, -L] == u[t, x, y, L],
    u[0, x, y, z] == Exp[-(x^2 + y^2 + z^2)],
    Derivative[1, 0, 0, 0][u][0, x, y, z] == 0},
   u, {t, 0, L/2}, {x, -L, L}, {y, -L, L}, {z, -L, L},
   MaxSteps -> {Infinity, ms, ms, ms}]


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