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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

On Computing of Eigenvalues of Differential Equations Q = λP with Eigenparameter in Boundary Conditions

S. M. Al-Harbi

Abstract

Problem statement: Our purpose of this study is to use sinc methods to compute approximately the eigenval-ues of second-order operator pencil of the form Q-λP. Approach: Where Q is second order self adjoint differential operator and P is a first order and λ∈C is an eigenvalue parameter. Results: The eigenparameter appears in the boundary conditions linearly. Using computable error boundswe obtain eigenvalue enclosures in a simple way. Conclusion/Recommendations: We give some numerical examples and makecompanions with existing results.

Journal of Mathematics and Statistics
Volume 7 No. 1, 2011, 28-36

DOI: https://doi.org/10.3844/jmssp.2011.28.36

Submitted On: 2 November 2010 Published On: 29 January 2011

How to Cite: Al-Harbi, S. M. (2011). On Computing of Eigenvalues of Differential Equations Q = λP with Eigenparameter in Boundary Conditions. Journal of Mathematics and Statistics, 7(1), 28-36. https://doi.org/10.3844/jmssp.2011.28.36

Open AccessCopyright: © 2011 S. M. Al-Harbi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Sinc method
  • operator pencil
  • eigenvalue problem
  • eigenparameter in boundary conditions
  • computing eigenvalues
  • Whittaker-Kotel'nikov-Shannon (WKS)