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Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method


Author: Bilal Chanane
Journal: Math. Comp. 74 (2005), 1793-1801
MSC (2000): Primary 34B24, 34L15, 34B07
DOI: https://doi.org/10.1090/S0025-5718-05-01717-5
Published electronically: March 18, 2005
MathSciNet review: 2164097
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Abstract: The purpose in this paper is to compute the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the regularized sampling method, an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost. A few examples shall be presented to illustrate the power of the method and a comparison made with the the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions.


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Additional Information

Bilal Chanane
Affiliation: Department of Mathematical Sciences, KFUPM, Dhahran 31261, Saudi Arabia
Email: chanane@kfupm.edu.sa

DOI: https://doi.org/10.1090/S0025-5718-05-01717-5
Keywords: Second order Sturm-Liouville problems, eigenvalue problems, Whittaker-Shannon-Kotel\textprime nikov theorem, parameter dependent boundary conditions, regularized sampling method
Received by editor(s): June 23, 2003
Received by editor(s) in revised form: March 18, 2004
Published electronically: March 18, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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