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    Potential Equation on a Disc : Dirichlet

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    Solve the potential equation on a disc...
    (See attachment for full question)

    © BrainMass Inc. brainmass.com March 4, 2021, 6:08 pm ad1c9bdddf
    https://brainmass.com/math/integrals/potential-equation-disc-dirichlet-30769

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    Solution:
    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)
    Let
    ( 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 ...

    Solution Summary

    The Potential Equation on a Disc is solved. The solution is detailed and well presented.

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