Re: Urgent

*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*: <dag0g8$5a3$1@smc.vnet.net>*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: > > http://mathematica.no.sapo.pt/index.html > 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 << Calculus`VectorAnalysis` SetCoordinates[OblateSpheroidal[theta, eta, phi, a]] F=F1[theta]*F2[eta]*F3[phi]] Laplacian[ F ]/F // FullSimplify // Expand 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. -- Roland Franzius