Approximation of eigenvalues of Sturm-Liouville problems by using Hermite interpolation
type: Item
instance of: scholarly article
title: Approximation of eigenvalues of Sturm-Liouville problems by using Hermite interpolation
zbMATH Open document ID: 1417.65142
DOI: 10.1155/2013/412028
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. In this paper, we use the derivative sampling theorem ``Hermite interpolations'' to compute approximate values of the eigenvalues of Sturm-Liouville problems with eigenvalue parameter in one or two boundary conditions. We use recently derived estimates for the truncation and amplitude errors to compute error bounds. Also, using computable error bounds, we obtain eigenvalue enclosures. Also numerical examples, which are given at the end of the paper, give comparisons with the classical sinc method and explain that the Hermite interpolations method gives remarkably better results.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L16
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 6306809
Wikidata QID: Q58916210
author: M. M. Tharwat
author: Saleh M. Al-Harbi
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/412028
OpenAlex ID: W1979381270
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description: scientific article; zbMATH DE number 6306809