A high-order BVM approach to computation of embedded eigenvalues in Sturm-Liouville problems

P. Ghelardoni, G. Gheri and M. Marletta
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P. Ghelardoni: Università di Pisa, Dipartimento di Matematica Applicata
G. Gheri: Università di Pisa, Dipartimento di Matematica Applicata
M. Marletta: University of Leicester, Department of Mathematics and Computer Science

A chapter in Numerical Mathematics and Advanced Applications, 2003, pp 891-898 from Springer

Abstract: Summary In this paper two classical methods to compute the numerical solution of a ³-rational Sturm-Liouville problem are analyzed in connection with the shooting technique: the method of Magnus series and the boundary value methods. We show that these methods display a weakening of their performances in the presence of an eigenvalue embedded in the essential spectrum. Nevertheless we show that some boundary value methods used in a particular form preserve their high order of convergence. Lastly we examine the performance of some boundary value methods applied to a singular problem when the Niessen-Zettl transformation is used.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-2089-4_80

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DOI: 10.1007/978-88-470-2089-4_80

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