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    Potential Equation on a Disc : Dirichlet

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    Solve the potential equation on a disc...
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    We have to solve a Dirichlet problem inside a circle of radius (c).
    The most usual method to do that is the Fourier method, that means using separation of variables.
    Let's process our equation and let's separate the variables:
    ( 1)
    ( 2)
    Introducing in (1), we will have

    ( 3)
    Why should we use a positive constant and not a negative one?
    Because using a negative constant, the ODE in (T) doesn't have periodic solutions, while our problem must have periodic solutions with ...

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