- To: mathgroup at smc.vnet.net
- Subject: [mg58550] Re: Urgent
- From: Roland Franzius <roland.franzius at uos.de>
- Date: Thu, 7 Jul 2005 05:35:39 -0400 (EDT)
- Organization: Universitaet Hannover
- References: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
Bruno Vicente wrote:
> I need help solving the Laplace equation in three dimensions using Mathematica. Due to the geometric configuration I used oblate and prolate spheroidal coordinates.
> You can see the equations I'm using in:
Particular solutions are possible as series of products of exponentials
in phi, Legendre polynomials of the first L^m_n kind of cos theta and
the second kind Q^m_n of cosh eta, also expressible by spherical
harmonics Y_lm(cos theta) * Q^m_n (cosh eta).
Make a product ansatz
SetCoordinates[OblateSpheroidal[theta, eta, phi, a]]
Laplacian[ F ]/F //
and separate the terms depending on one variable only. You have to solve
three eigenvalue ODE's and then you select the fourier sum over the
eigenvalue-indexed products to fit your boundary values.
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