Numerical Algorithms

, Volume 63, Issue 1, pp 27–48 | Cite as

Numerical computation of eigenvalues of discontinuous Sturm–Liouville problems with parameter dependent boundary conditions using sinc method

Original Paper

Abstract

In this paper, we consider a Sturm–Liouville problem which contains an eigenparameter appearing linearly in two boundary conditions, in addition to an internal point of discontinuity. Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. We apply the sinc method, which is based on the sampling theory to compute approximations of the eigenvalues. An error analysis is exhibited involving rigorous error bounds. Using computable error bounds we obtain eigenvalue enclosures in a simple way. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

Keywords

Sturm–Liouville problems Discontinuity conditions Sinc methods Error analysis 

Mathematics Subject Classifications (2010)

34L16 94A20 65L15 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • M. M. Tharwat
    • 1
    • 2
  • A. H. Bhrawy
    • 1
    • 2
  • Ahmet Yildirim
    • 3
  1. 1.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt
  3. 3.Urla-IzmirTurkey

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