Hey guys
I am trying to solve this Poisson equation, but i can't get a break through. Has anyone solved this before? I can't find ONE single example, where f instead of 0 (zero) is a pure function f(x,y). The main thing here is, that the problem has to be solved using Fourier series... This is the only good example I've found (http://math.la.asu.edu/~kuiper/502files/Laplace.pdf) but it's not explained how they got Umn,...
\(\displaystyle \Delta\, u=\,1,\, (x,y)\, \epsilon \,D,\,u(x,y)\,=\,0,\,(x,y)\,\epsilon\,\partial\,D\)
Basically, we're solving \(\displaystyle u_{xx}\,+\,u_{yy}\,=\,1\)
One possible solution for u is: \(\displaystyle u(x,y)\,=\,\frac{x^{2}\,+\,y^{2}}{4}\)
But the solution should be expanded into Fourier series, so I got stuck there. Hope someone will know how to solve this...
I am trying to solve this Poisson equation, but i can't get a break through. Has anyone solved this before? I can't find ONE single example, where f instead of 0 (zero) is a pure function f(x,y). The main thing here is, that the problem has to be solved using Fourier series... This is the only good example I've found (http://math.la.asu.edu/~kuiper/502files/Laplace.pdf) but it's not explained how they got Umn,...
\(\displaystyle \Delta\, u=\,1,\, (x,y)\, \epsilon \,D,\,u(x,y)\,=\,0,\,(x,y)\,\epsilon\,\partial\,D\)
Basically, we're solving \(\displaystyle u_{xx}\,+\,u_{yy}\,=\,1\)
One possible solution for u is: \(\displaystyle u(x,y)\,=\,\frac{x^{2}\,+\,y^{2}}{4}\)
But the solution should be expanded into Fourier series, so I got stuck there. Hope someone will know how to solve this...
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