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We show that one can derive an O(N 3) spectral-Galerkin method for fourth order (biharmonic type) elliptic equations based on the use of Chebyshev polynomials. The use of Chebyshev polynomials provides a fast transform between physical and spectral space which is advantageous when a sequence of problems must be solved e.g., as part of a nonlinear iteration.… (More)

We solve the biharmonic eigenvalue problem 2 u = u and the buckling plate problem 2 u = ?u on the unit square using a highly accurate spectral Legendre-Galerkin method. We study the nodal lines for the rst eigenfunction near a corner for the two problems. Five sign changes are computed and the results show that the eigenfunction exhibits a self similar… (More)

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