Computing Eigenvalues of Discontinuous Sturm-Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite Approximation

The eigenvalues of discontinuous Sturm-Liouville problems which contain an eigenparameter appearing linearly in two boundary conditions and an internal point of discontinuity are computed using the derivative sampling theorem and Hermite interpolations methods. We use recently derived estimates for...

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Main Authors: M. M. Tharwat, A. H. Bhrawy, A. S. Alofi
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/498457
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author M. M. Tharwat
A. H. Bhrawy
A. S. Alofi
author_facet M. M. Tharwat
A. H. Bhrawy
A. S. Alofi
author_sort M. M. Tharwat
collection DOAJ
description The eigenvalues of discontinuous Sturm-Liouville problems which contain an eigenparameter appearing linearly in two boundary conditions and an internal point of discontinuity are computed using the derivative sampling theorem and Hermite interpolations methods. We use recently derived estimates for the truncation and amplitude errors to investigate the error analysis of the proposed methods for computing the eigenvalues of discontinuous Sturm-Liouville problems. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented. Moreover, it is shown that the proposed methods are significantly more accurate than those based on the classical sinc method.
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series Abstract and Applied Analysis
spelling doaj-art-de7eb62546024946b4bed74dd6f4d3ee2025-08-20T02:21:21ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/498457498457Computing Eigenvalues of Discontinuous Sturm-Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite ApproximationM. M. Tharwat0A. H. Bhrawy1A. S. Alofi2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaThe eigenvalues of discontinuous Sturm-Liouville problems which contain an eigenparameter appearing linearly in two boundary conditions and an internal point of discontinuity are computed using the derivative sampling theorem and Hermite interpolations methods. We use recently derived estimates for the truncation and amplitude errors to investigate the error analysis of the proposed methods for computing the eigenvalues of discontinuous Sturm-Liouville problems. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented. Moreover, it is shown that the proposed methods are significantly more accurate than those based on the classical sinc method.http://dx.doi.org/10.1155/2013/498457
spellingShingle M. M. Tharwat
A. H. Bhrawy
A. S. Alofi
Computing Eigenvalues of Discontinuous Sturm-Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite Approximation
Abstract and Applied Analysis
title Computing Eigenvalues of Discontinuous Sturm-Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite Approximation
title_full Computing Eigenvalues of Discontinuous Sturm-Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite Approximation
title_fullStr Computing Eigenvalues of Discontinuous Sturm-Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite Approximation
title_full_unstemmed Computing Eigenvalues of Discontinuous Sturm-Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite Approximation
title_short Computing Eigenvalues of Discontinuous Sturm-Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite Approximation
title_sort computing eigenvalues of discontinuous sturm liouville problems with eigenparameter in all boundary conditions using hermite approximation
url http://dx.doi.org/10.1155/2013/498457
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AT ahbhrawy computingeigenvaluesofdiscontinuoussturmliouvilleproblemswitheigenparameterinallboundaryconditionsusinghermiteapproximation
AT asalofi computingeigenvaluesofdiscontinuoussturmliouvilleproblemswitheigenparameterinallboundaryconditionsusinghermiteapproximation