Chebyshev Polynomial Approximations for the L -Membrane Eigenvalue Problem
J. C. Mason
Source abstract
In this paper a new method is proposed for the solution of partial differential equations in terms of two-dimensional Chebyshev series. The method is a generalization of the “selected points” method described by C. Lanczos [3] for solving ordinary differential equations. Some indications are given of the possible applications of the method, and it is applied in detail to a particular example, the eigenvalue problem for a vibrating L-shaped membrane. The work involved in computation is much the same as for finite difference methods of solving the problem, but our method seems to be simpler to apply and eigenfunctions are obtained in a convenient form.
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