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

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • P. Ghelardoni & G. Gheri & M. Marletta, 2003. "A high-order BVM approach to computation of embedded eigenvalues in Sturm-Liouville problems," Springer Books, in: Franco Brezzi & Annalisa Buffa & Stefania Corsaro & Almerico Murli (ed.), Numerical Mathematics and Advanced Applications, pages 891-898, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2089-4_80
    DOI: 10.1007/978-88-470-2089-4_80
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