Qualitative behaviour of numerical approximations to Volterra integro-differential equations
type: Item
instance of: scholarly article
title: Qualitative behaviour of numerical approximations to Volterra integro-differential equations
zbMATH Open document ID: 1059.65129
author: Yihong Song
author: Christopher T. H. Baker
published in: Journal of Computational and Applied Mathematics
publication date: 2004-10-12T00:00:00Z
review text: The authors consider the numerical solution of a nonlinear Volterra integro-differential equation with infinite delay under numerical approximation. The equation arises as a single-species growth model and the numerical method under consideration is the composite \(\theta\) rule. The aim of the paper is to check that the qualitative behaviour of the numerical scheme reflects accurately the underlying qualitative behaviour of the original equation and to give conditions, if necessary, for this to happen. The application of a numerical method leads to a Volterra difference scheme and the authors analyse the qualitative behaviour of the difference equations. They conclude that, for small enough step sizes and for small bounded initial function, the numerical scheme reflects accurately the behaviour of the exact solution. They point out that their analysis can also be applied to other classes of equations.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 2107319
zbMATH Keywords: infinite delay
zbMATH Keywords: numerical stability
zbMATH Keywords: nonlinear Volterra integro-differential equation
zbMATH Keywords: Volterra difference scheme
reviewed by: Neville J. Ford
MaRDI profile type: Publication
full work available at URL: j.cam.2003.12.049
OpenAlex ID: W2171713632
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DOI: 10.1016/J.CAM.2003.12.049
description: scientific article; zbMATH DE number 2107319