Numerical stability analysis of steady state solutions of integral equations with distributed delays
type: Item
instance of: scholarly article
title: Numerical stability analysis of steady state solutions of integral equations with distributed delays
zbMATH Open document ID: 1052.65119
author: Tatyana Luzyanina
author: Dirk Roose
author: Koen Engelborghs
published in: Applied Numerical Mathematics
publication date: 2004-08-10T00:00:00Z
review text: The authors consider the delay integral equation \[ y(t)=a\int_{t-\tau}^t K(t-\xi)y(\xi)d\xi \] under a discrete scheme based on Lagrange interpolation and a Gauss-Legendre quadrature rule. The aim of the paper is to establish conditions under which the true stability of the underlying equation is preserved in the discrete scheme. The paper is structured as follows: after an initial introduction, the authors describe their discrete scheme, they review the stability properties of the zero solution of the integral equation and deduce results relating the properties of the zero solution of the discrete analogue. Their detailed investigations lead to conjectures about the preservation of stability in discrete analogue equation. The results of numerical experiments are reported.
reviewed by: Neville J. Ford
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45M10
zbMATH DE Number: 2085828
zbMATH Keywords: numerical stability analysis
zbMATH Keywords: distributed delays
zbMATH Keywords: delay integral equation
zbMATH Keywords: Lagrange interpolation
zbMATH Keywords: Gauss-Legendre quadrature rule
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.apnum.2003.12.001
OpenAlex ID: W1980410774
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DOI: 10.1016/J.APNUM.2003.12.001
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description: scientific article; zbMATH DE number 2085828