Laplace equation

  • Thread starter Aamodt
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Hi, I'm trying to solve the Laplace equatio in oblate and prolate spheroidal coordinates, but it's proving to be too much for me to handle, can anyone help me out?
You can see the equations I'm using in:
http://mathematica.no.sapo.pt/index.html
 
Last edited:

dextercioby

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I "Cannot find server". Can you attach a written document with your work...?

Daniel.
 
I have corrected the problem, you can now access the web page with the equations, thanks for the warning.
 

lurflurf

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Aamodt said:
Hi, I'm trying to solve the Laplace equatio in oblate and prolate spheroidal coordinates, but it's proving to be too much for me to handle, can anyone help me out?
You can see the equations I'm using in:
http://mathematica.no.sapo.pt/index.html
Laplaces equation for what (scalar, vector, tensor rank-2?). Using what method (numerical solution, separation of variable, integral transforms?).
I would guess that you intend to solve the scalar laplace equation using seperation of variables. So you presume the solution can be written in the form of a sum of terms that are products of functions of one variable. Then the partial differential equation implies that the functions of one variable satisfy some strum louiville problem.
Mathworld says your two systems are among the 13 where laplaces equation can be solved by separation of variables and that solutions involve Legendre polynomials and circular functions. In any case you are looking at some messy algebra and calculus.

http://mathworld.wolfram.com/LaplacesEquation.html
 

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