Symmetrization of the sinc-Galerkin method for boundary value problems

Author:
John Lund

Journal:
Math. Comp. **47** (1986), 571-588

MSC:
Primary 65N30; Secondary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856703-9

MathSciNet review:
856703

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Abstract: The Sinc-Galerkin method developed in [5], when applied to the second-order selfadjoint boundary value problem, gives rise to a nonsymmetric coefficient matrix. The technique in [5] is based on weighting the Galerkin inner products in such a way that the method will handle boundary value problems with regular singular points. In particular, the method does an accurate job of handling problems with singular solutions (the first or a higher derivative of the solution is unbounded at one or both of the boundary points). Using *n* function evaluations, the method of [5] converges at the rate , where *k* is independent of *n*. In this paper it is shown that, by changing the weight function used in the Galerkin inner products, the coefficient matrix can be made symmetric. This symmetric method is applicable to a slightly more restrictive set of boundary value problems than the method of [5], The present method, however, still handles a wide class of singular problems and also has the same convergence rate.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856703-9

Article copyright:
© Copyright 1986
American Mathematical Society