Numerical computation of eigenvalues of discontinuous Sturm–Liouville problems with parameter dependent boundary conditions using sinc method

In this paper, we consider a Sturm–Liouville problem which contains an eigenparameter appearing linearly in two boundary conditions, in addition to an internal point of discontinuity. Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic...

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Bibliographic Details
Published in:Numerical algorithms Vol. 63; no. 1; pp. 27 - 48
Main Authors: Tharwat, M. M., Bhrawy, A. H., Yildirim, Ahmet
Format: Journal Article
Language:English
Published: Boston Springer US 01.05.2013
Springer Nature B.V
Subjects:
Algebra
Algorithms
Approximation
Boundary conditions
Computer Science
Discontinuity
Eigenvalues
Error analysis
Mathematical models
Numeric Computing
Numerical Analysis
Original Paper
Sampling
Theory of Computation
Error analysis
65L15
34L16
Sinc methods
Discontinuity conditions
Sturm–Liouville problems
94A20
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper, we consider a Sturm–Liouville problem which contains an eigenparameter appearing linearly in two boundary conditions, in addition to an internal point of discontinuity. Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. We apply the sinc method, which is based on the sampling theory to compute approximations of the eigenvalues. An error analysis is exhibited involving rigorous error bounds. Using computable error bounds we obtain eigenvalue enclosures in a simple way. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-012-9609-3