Stability of BDF methods for nonlinear Volterra integral equations with delay
type: Item
instance of: scholarly article
title: Stability of BDF methods for nonlinear Volterra integral equations with delay
zbMATH Open document ID: 1007.65112
DOI: 10.1016/S0898-1221(01)00275-9
publication date: 2002-08-15T00:00:00Z
review text: The authors consider the nonlinear delay Volterra integral equation with constant delay \(\tau> 0\), \[ y(t)= g(t)+ \int^t_0 f(\xi, y(\xi), y(\xi- \tau)) d\xi,\quad t> 0, \] with \(y(t)= \phi(t)\), \(t\in [-\tau, 0]\). Here, \(f= f(s,y,z)\) (which does not depend on \(t\)) is subjet to certain non-classical (one-sided) Lipschitz conditions. Its solution is approximated by the backward differentiation formula (BDF) method on a uniform mesh, using an implementation based on \textit{B. Cahlon} [J. Comput. Appl. Math. 33, No. 1, 97-104 (1990; Zbl 0719.65092)]. The asymptotic stability analysis is based on Dahlquist's concept of \(G\)-stability which is extended to what the authors call \(G(c,p,q)\)-stability for the resulting discrete Volterra equation.
reviewed by: H. Brunner
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 1781461
zbMATH Keywords: backward differentiation formula method
zbMATH Keywords: nonlinear delay Volterra integral equation
zbMATH Keywords: asymptotic stability
zbMATH Keywords: \(G\)-stability
author: Cheng-Jian Zhang
author: Xiaoxin Liao
MaRDI profile type: Publication
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full work available at URL: s0898-1221(01)00275-9
OpenAlex ID: W2072946708
Wikidata QID: Q126643946
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1781461