\(\mathcal H\)-stability of linear \(\theta\)-method with general variable stepsize for system of pantograph equations with two delay terms
type: Item
instance of: scholarly article
title: \(\mathcal H\)-stability of linear \(\theta\)-method with general variable stepsize for system of pantograph equations with two delay terms
zbMATH Open document ID: 1071.65102
author: Yang Xu
author: M. Z. Liu
published in: Applied Mathematics and Computation
publication date: 2004-11-23T00:00:00Z
review text: The authors study the two-dimensional linear pantograph equation \(\dot x(t)= a_1 x(t)+b_1 y(q_1t)\), \(\dot y(t)=a_2 y(t)+b_2 x(q_2t)\) for \(0<q_1\leq q_2<1\). The authors first give sufficient conditions on the complex system parameters \(a_j\), \(b_j\) (\(j=1,2\)) such that the origin is globally asymptotically stable independent of \(q_1\) and \(q_2\). Then, they prove that the linear \(\theta\)-method with variable stepsize is \({\mathcal H}\)-stable if \(1/2<\theta<1\). \({\mathcal H}\)-stability means that all numerical solutions tend to zero if the origin is asymptotically stable regardless of \(q_1\), \(q_2\), and the sequence of stepsizes.
reviewed by: Jan Sieber
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 2118011
zbMATH Keywords: delay differential equations
zbMATH Keywords: infinite lag
zbMATH Keywords: stability
zbMATH Keywords: linear pantograph equation
zbMATH Keywords: variable stepsize
zbMATH Keywords: theta-method
MaRDI profile type: Publication
full work available at URL: j.amc.2003.06.008
OpenAlex ID: W2030846838
cites work: Asymptotic stability properties of \(\theta\)-methods for the pantograph equation
cites work: On the contractivity and asymptotic stability of systems of delay differential equations of neutral type
cites work: On the dynamics of a discretized neutral equation
cites work: Stability of the Discretized Pantograph Differential Equation
cites work: On the asymptotic stability of \(\theta\)-methods for delay differential equations
cites work: Matrix Analysis
cites work: A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
cites work: Q4839883
cites work: Stability analysis of Runge-Kutta methods for systems of delay differential equations
cites work: Stability analysis of numerical methods for delay differential equations
cites work: On the generalized pantograph functional-differential equation
cites work: Q4839870
cites work: Exact and discretized stability of the pantograph equation
cites work: Stability of Runge-Kutta methods for the generalized pantograph equation
cites work: Monotonic and Oscillatory Solutions of a Linear Neutral Delay Equation with Infinite Lag
cites work: The Stability of the θ-methods in the Numerical Solution of Delay Differential Equations
cites work: Stability analysis of \(\theta\)-methods for neutral functional- differential equations
cites work: On the \(\theta\)-method for delay differential equations with infinite lag
cites work: Asymptotic behaviour of functional-differential equations with proportional time delays
cites work: Numerical investigation of the pantograph equation
cites work: Numerical stability of the \(\theta\)-methods for systems of differential equations with several delay terms
cites work: Stability of numerical methods for delay differential equations
DOI: 10.1016/J.AMC.2003.06.008
description: scientific article; zbMATH DE number 2118011