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Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials. (English) Zbl 1103.65119
The authors are concerned with the efficiency of spectral-Galerkin methods in solving second order boundary value problems. Specifically, they use the Jacobi polynomials in order to construct shape functions bases. These bases satisfy the boundary conditions and, at the same time, lower the condition number of the accompanying matrices with two orders. Some numerical examples are carried out to underline the reliability of the chosen bases.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65F05 Direct numerical methods for linear systems and matrix inversion
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F35 Numerical computation of matrix norms, conditioning, scaling
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