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

Chanane, Bilal

doi:10.1090/S0025-5718-05-01717-5

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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