Hi. I have this problem in trying to solve this PDE analytically.(adsbygoogle = window.adsbygoogle || []).push({});

The PDE is represented by this diagram:

Basically this is solving the Laplace equation with those insulated boundaries except it has that point diffusing its value across the plane. I know how to solve the Laplace equation part. The problem is that I do not know how to solve the Laplace equation WITH a single point in there located at point (x_{i}, y_{i}).

While I have no problem in trying to solve this using numerical analysis, I am totally clueless how to solve this analytically. Where should I start? What should I do?

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# A 2D Cartesian Laplace equation with a single point diffusion

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