Stability properties of a scheme for the approximate solution of a delay- integro-differential equation
type: Item
instance of: scholarly article
title: Stability properties of a scheme for the approximate solution of a delay- integro-differential equation
zbMATH Open document ID: 0754.65111
DOI: 10.1016/0168-9274(92)90027-B
author: Christopher T. H. Baker
author: Neville J. Ford
published in: Applied Numerical Mathematics
publication date: 1992-09-26T00:00:00Z
review text: The authors study stability properties of a numerical scheme applied to Volterra integro-differential equations with finite memory of the form \(y'(t)=G(t,y(t),\int^ t_{t-\tau}K(t,s,y(s))ds\), \(t\geq 0\), \(y(t)=\psi(t)\), \((-\tau\leq t<0)\), where \(G\), \(K\) and \(\psi\) are given smooth functions. This numerical scheme is based on a strongly-stable linear multistep formula and a consistent quadrature rule.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 54686
zbMATH Keywords: quadrature method
zbMATH Keywords: stability
zbMATH Keywords: Volterra integro-differential equations with finite memory
zbMATH Keywords: strongly-stable linear multistep formula
zbMATH Keywords: consistent quadrature rule
Wikidata QID: Q115363736
MaRDI profile type: Publication
cites work: Q3804137
cites work: Q3750978
cites work: Nonlinear Volterra integrodifferential systems with L\(^1\)-kernels
cites work: On the Stability of Linear Multistep Methods for Volterra Convolution Equations
cites work: Theory of difference equations: Numerical methods and applications
cites work: Asymptotic stability properties of linear Volterra integrodifferential equations
cites work: Q4195836
cites work: Q5673119
full work available at URL: 0168-9274(92)90027-b
OpenAlex ID: W1970448574
description: scientific article; zbMATH DE number 54686