Sinc approximation of eigenvalues of Sturm–Liouville problems with a Gaussian multiplier

Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. Sampling theory is one of the most important mathematical tools used in communication engineering since it enables engineers to...

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Bibliographic Details
Published in:Calcolo 2014-09, Vol.51 (3), p.465-484
Main Author: Tharwat, M. M.
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Decay
Eigenvalues
Gaussian
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Normal distribution
Numerical Analysis
Sampling
Theory of Computation
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Summary:Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. Sampling theory is one of the most important mathematical tools used in communication engineering since it enables engineers to reconstruct signals from some of their sampled data. The sinc Gaussian sampling technique derived by Qian (Proc Am Math Soc 131:1169–1176, 2002 ) establishes a sampling technique which converges faster than the classical sampling technique. Schmeisser and Stenger (Sampl Theory Signal Image Process 6:199–221, 2007 ) studied the associated error analysis. In the present paper we apply a sinc Gaussian technique to compute approximate values of the eigenvalues of Sturm–Liouville problems with eigenvalue parameter in one or two boundary conditions. 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 the classical sinc method. Numerical worked examples with tables and illustrative figures are given at the end of the paper.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-013-0095-3