Re: NDSolve with 3 independent variables

• To: mathgroup at smc.vnet.net
• Subject: [mg122741] Re: NDSolve with 3 independent variables
• From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
• Date: Tue, 8 Nov 2011 07:16:59 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201111071052.FAA03762@smc.vnet.net>

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}]

Oliver

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