Asymptotic stability of solutions to Volterra-renewal integral equations with space maps
type: Item
instance of: scholarly article
title: Asymptotic stability of solutions to Volterra-renewal integral equations with space maps
zbMATH Open document ID: 1254.45012
author: H. Brunner
author: E. Messina
author: M. Annunziato
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-08-30T00:00:00Z
reviewed by: Alexander N. Tynda
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 6074425
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: linear Volterra-renewal integral equations
zbMATH Keywords: stability
zbMATH Keywords: direct quadrature
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.jmaa.2012.05.080
OpenAlex ID: W1984738960
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DOI: 10.1016/J.JMAA.2012.05.080
review text: The following linear Volterra-renewal integral equations are considered NEWLINE\[NEWLINE u(x,t)=f(x,t)+\int\limits_{0}^{t}k(t-\eta)u(g(x,t,\eta),\eta)d\eta, NEWLINE\]NEWLINE with \(t>0,\:x\in\Omega:=[a,b]\), where \(k(t)\geq 0,\:f(x,t)\geq 0\) and \(g(x,t,\eta)\) are known continuous functions. Their solutions depend on the space variable, via a map transformation.NEWLINENEWLINEThe authors investigate the asymptotic behavior of these solutions, and study the asymptotic stability of a numerical method based on direct quadrature in time and interpolation in space. There are also some numerical experiments showing that this method behaves according to the theoretical results.
description: scientific article; zbMATH DE number 6074425