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Solving the Laplace Equation in 2D with NDSolve

Posted 9 years ago

Dear community members,

I am trying to solve the Laplace equation in cylindrical coordinates using NDSolve. (By the way, I am aware that there is an analytical solution for this problem in terms of Fourier-Bessel series, but I thought this is a good opportunity to see how Mathematica handles such problems.) In the attached file you can see how I tried to do it. I checked and double-checked my code but I cannot find the source of my error. Neither of the two error messages make any sense to me. (Error message #1: "the system is overdetermined".... I don't see why.) (Error message #2: "NDSolve is not a replacement rule etc".... That is probably because this line was not executed in the first place.)

Can anybody tell me where I go astray?

Thanks in advance, René Samson

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POSTED BY: Rene Samson
3 Replies
Posted 9 years ago

Dear Gianluca, dear Frank, gents,

You were both "spot-on". 1. The unboundedness of the domain was the problem. 2. And I would quickly have found that out if I had simplified the problem. For your entertainment I enclose the "corrected" Notebook, which shows that if I replace the upper limit by a large number, Mathematica finds the solution without any problems.

Thanks for your swift reactions, René Samson

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POSTED BY: Rene Samson

Have you tried solving a simpler version of your problem?

POSTED BY: Frank Kampas

I am not expert in PDE, but I wonder if Mathematica can handle numerical PDEs on unbounded domains.

I would rewrite the deffinition of the function c0 with Piecewise, instead of If.

POSTED BY: Gianluca Gorni
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