The FD-method for solving Sturm-Liouville problems with special singular differential operator

Makarov, V.; Dragunov, D.; Klimenko, Ya.

doi:10.1090/S0025-5718-2012-02634-2

The FD-method for solving Sturm-Liouville problems with special singular differential operator
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by V. L. Makarov, D. V. Dragunov and Ya. V. Klimenko PDF

Math. Comp. 82 (2013), 953-973 Request permission

Abstract:

A superexponentially convergent method for solving the Sturm-Liouville problem with Legendre’s differential operator is given. The presented method (called the FD-method) is based on the coefficient approximation methods (CAM) and the homotopy approach. Sufficient convergence conditions of the proposed method are stated and rigorously substantiated. The algorithms for software implementation of the proposed method are described. The numerical examples included in the paper confirm the theoretical conclusions.

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