Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations
type: Item
instance of: scholarly article
title: Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations
zbMATH Open document ID: 0886.65092
published in: Numerische Mathematik
publication date: 1997-12-10T00:00:00Z
review text: The initial value problem for a system of delay differential equations and its approximate solution by means of RN-stable continuous Runge-Kutta methods are considered. The notion of RN-stability has been introduced recently by \textit{L. Torelli} [J. Comput. Appl. Math. 25, No. 1, 15-26 (1989; Zbl 0664.65073)] for numerical methods applied to dissipative nonlinear systems of delay differential equations. The authors show that RN-stable Runge-Kutta methods also preserve this asymptotic stability property. Essentially, RN-stability ensures that even the discrete solution possesses the contractivity property known from the analytic solution.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1096029
zbMATH Keywords: system
zbMATH Keywords: delay differential equations
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: RN-stability
zbMATH Keywords: asymptotic stability
author: M. Zennaro
reviewed by: Etienne Emmrich
MaRDI profile type: Publication
full work available at URL: s002110050300
OpenAlex ID: W1982536042
DOI: 10.1007/S002110050300
description: scientific article; zbMATH DE number 1096029