Asymptotic behavior of solutions to a Volterra integro-differential equation
type: Item
instance of: scholarly article
title: Asymptotic behavior of solutions to a Volterra integro-differential equation
zbMATH Open document ID: 0683.45004
DOI: 10.1216/JIE-1988-1-4-501
author: Martin Klaus
author: Zdzislaw Jackiewicz
author: Colm Art O'Cinneide
published in: Journal of Integral Equations and Applications
publication date: 1988-01-01T00:00:00Z
review text: The authors study the asymptotic behaviour of solutions of Volterra integro-differential equations of the form \((*)\quad y'(t)=\gamma y(t)+\int^{t}_{0}(\lambda +\mu t+\nu s)y(s)ds,\) \(y(0)=1\), \(t\geq 0\), where \(\gamma\), \(\lambda\), \(\mu\) and \(\nu\) are real parameters such that \(\mu +\nu \neq 0\), through the related ordinary differential equations \(y\prime''=\gamma y''+(\lambda +(\mu +\nu)t)y'+(2\mu +\nu)y.\) They obtain sufficient conditions for the boundedness of the exact solution of (*). This enables them to compare the exact solution with the approximate solutions of (*) resulting from the application of reducible linear multistep methods and modified multilag methods. A numerical example is given to illustrate their results.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 4118957
zbMATH Keywords: bounded solution
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: Volterra integro-differential equations
zbMATH Keywords: reducible linear multistep methods
zbMATH Keywords: multilag methods
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: jie-1988-1-4-501
OpenAlex ID: W1987639650
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description: scientific article; zbMATH DE number 4118957