Using a (Higher-Order) Magnus Method to Solve the Sturm-Liouville Problem

Authors:
Veerle Ledoux;Marnix Daele;Guido Berghe
Affiliations:
Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Gent, Belgium B-9000;Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Gent, Belgium B-9000;Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Gent, Belgium B-9000
Venue:
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
Year:
2008

Citing 3
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Abstract

The main purpose of this paper is to describe techniques for the numerical solution of a Sturm-Liouville equation (in its Schrödinger form) by employing a Magnus expansion. With a suitable method to approximate the highly oscillatory integrals which appear in the Magnus series, high order schemes can be constructed. A method of order ten is presented. Even when the solution is highly-oscillatory, the scheme can accurately integrate the problem using stepsizes typically much larger than the solution "wavelength". This makes the method well suited to be applied in a shooting process to locate the eigenvalues of a boundary value problem.