Research Article Open Access

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

S. M. Al-Harbi1
  • 1 ,
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

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.

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Keywords

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