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A direct solver for the Legendre tau approximation for the two-dimensional Poisson problem. (English) Zbl 1115.65121

A direct solver for the Legendre tau approximation for the two-dimensional Poisson problem is proposed. Using the factorization of a symmetric eigenvalue problem, the algorithm overcomes the weak points of the Schur decomposition. The convergence is shown and numerical results are presented.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

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References:

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