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
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,
Have you tried solving a simpler version of your problem?
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.