Sinc Function computation of the eigenvalues of Sturm-Liouville problems
type: Item
instance of: scholarly article
title: Sinc Function computation of the eigenvalues of Sturm-Liouville problems
zbMATH Open document ID: 0618.65073
DOI: 10.1016/0021-9991(87)90163-X
author: Mary Jarratt
author: Norman H. Eggert
author: John R. Lund
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
review text: The sinc function is defined by \(\sin c(t)=\sin (\pi t)/\pi t,\) \(t\in (- \infty,\infty)\). As one of the applications of this function, the authors develop a collocation scheme using sinc basis functions to approximate the eigenvalues of regular and singular Sturm-Liouville boundary value problems. Utilizing a conformal map of the given connected domain onto the infinite strip, the error in the approximation of the eigenvalues is shown to converge at the rate exp(-\(\alpha\sqrt{N})\) \((\alpha >0)\), where \(2N+1\) basis elements in the collocation scheme is used. A number of numerical test examples are included (for both finite and infinite interval) to indicate the accuracy and the implementation of the method.
reviewed by: Taketomo Mitsui
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L99
zbMATH DE Number: 4003408
zbMATH Keywords: sinc function
zbMATH Keywords: collocation scheme
zbMATH Keywords: eigenvalues
zbMATH Keywords: Sturm-Liouville boundary value problems
zbMATH Keywords: numerical test examples
MaRDI profile type: Publication
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full work available at URL: 0021-9991(87)90163-x
OpenAlex ID: W2085351451
description: scientific article; zbMATH DE number 4003408