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Abstract and Applied Analysis
Volume 2013, Article ID 412028, 14 pages
http://dx.doi.org/10.1155/2013/412028
Research Article

Approximation of Eigenvalues of Sturm-Liouville Problems by Using Hermite Interpolation

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni Suef, Egypt
3Department of Mathematics, University College, Umm Al-Qura University, P.O. Box 8140, Makkah, Saudi Arabia

Received 5 August 2013; Accepted 21 September 2013

Academic Editor: Dumitru Baleanu

Copyright © 2013 M. M. Tharwat and S. M. Al-Harbi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. In this paper, we use the derivative sampling theorem “Hermite interpolations” to compute approximate values of the eigenvalues of Sturm-Liouville problems with eigenvalue parameter in one or two boundary conditions. We use recently derived estimates for the truncation and amplitude errors to compute error bounds. Also, using computable error bounds, we obtain eigenvalue enclosures. Also numerical examples, which are given at the end of the paper, give comparisons with the classical sinc method and explain that the Hermite interpolations method gives remarkably better results.