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So solution of Poisson's equation involves the following steps
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1) Find the Fourier coefficients fjk of f(x,y) by performing integral
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2) Form the Fourier coefficients of ? by ?jk = fjk / (-p2j2 - p2k2)
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3) Construct the solution by performing sum ?(x,y)
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There is another version of this (Discrete Fourier Transform) which deals with functions defined at grid points and not directly the continuous integral
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Also the simplest (mathematically) transform uses exp(-2pijx) not sin(p jx)
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Let us first consider 1D discrete version of this case
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PDE case normally deals with discretized functions as these needed for other parts of problem
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