Stability of Runge-Kutta methods in the numerical solution of equation \(u'(t)=au(t)+a_{0} u([t])+a_{1} u([t-1])\)
type: Item
instance of: scholarly article
title: Stability of Runge-Kutta methods in the numerical solution of equation \(u'(t)=au(t)+a_{0} u([t])+a_{1} u([t-1])\)
zbMATH Open document ID: 1063.65070
author: Z. W. Yang
author: Minghui Song
author: M. Z. Liu
published in: Applied Mathematics and Computation
publication date: 2005-02-22T00:00:00Z
review text: The authors discuss the numerical solution of the initial value problem \(u'(t) = a u(t) + a_0 u([t]) + a_1 u([t-1])\), \(u(0) = u_0\), \(u(-1) = u_{-1}\), where \([\cdot]\) denotes the floor function (round down to nearest integer). This is a special case of a delay differential equation with piecewise continuous argument. The numerical methods under consideration are of Runge-Kutta type. The authors first explain how standard Runge-Kutta methods can be applied to this class of problems. Then, the asymptotic stability of various special types of Runge-Kutta methods (e.g., Gauss, Lobatto, and Radau) is investigated.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34K28
zbMATH DE Number: 2136152
zbMATH Keywords: delay differential equation
zbMATH Keywords: piecewise continuous argument
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: asymptotic stability
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: j.amc.2003.12.081
OpenAlex ID: W2079857807
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DOI: 10.1016/J.AMC.2003.12.081
description: scientific article; zbMATH DE number 2136152