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Approximation of eigenvalues of discontinuous Sturm-Liouville problems with eigenparameter in all boundary conditions

Mohammed M Tharwat1*, Ali H Bhrawy12 and Abdulaziz S Alofi1

Author Affiliations

1 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

2 Permanent address: Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

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Boundary Value Problems 2013, 2013:132  doi:10.1186/1687-2770-2013-132

Published: 20 May 2013

Abstract

In this paper, we apply a sinc-Gaussian technique to compute approximate values of the eigenvalues of Sturm-Liouville problems which contain an eigenparameter appearing linearly in two boundary conditions, in addition to an internal point of discontinuity. The error of this method decays exponentially in terms of the number of involved samples. Therefore the accuracy of the new technique is higher than that of the classical sinc method. Numerical worked examples with tables and illustrative figures are given at the end of the paper.

MSC: 34L16, 94A20, 65L15.

Keywords:
sampling theory; Sturm-Liouville problems; transmission conditions; sinc-Gaussian; sinc method; truncation and amplitude errors