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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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2013; no. 2013; pp. 815 - 828-599
Main Authors Tharwat, M. M., Bhrawy, Ali H., Alofi, Abdulaziz
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2013
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Approximation
Boundary conditions
Boundary value problems
Computation
Derivatives
Discontinuity
Eigenvalues
Error analysis
Functions, Discontinuous
Interpolation
Mathematical research
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Summary: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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ISSN:1085-3375
1687-0409
DOI:10.1155/2013/498457