Nonlinear stability of Runge-Kutta methods applied to infinite-delay-differential equations
type: Item
instance of: scholarly article
title: Nonlinear stability of Runge-Kutta methods applied to infinite-delay-differential equations
zbMATH Open document ID: 1068.65106
DOI: 10.1016/S0895-7177(04)90520-1
author: Geng Sun
author: Cheng-Jian Zhang
published in: Mathematical and Computer Modelling
publication date: 2005-02-22T00:00:00Z
review text: The infinite delay-differential equation \[ \begin{gathered} y^1(t)= f(t, y(t), y(pt)),\qquad t> 0,\\ y(0)= \mu\end{gathered} \] is studied in \(\mathbb{C}^d\), where \(p\in (0,1)\), \(f(t,y,z)\) is contractive with constants \(\alpha\) and \(\beta\) toward \(y\) and \(z\), respectively, and \(\beta\leq p\alpha\). The authors divide \([0,\infty]\) into a sum of subintervals \(D_q= (T_q, T_{q+1}]\) and apply a Runge-Kutta \((k, 1)\)-algebraically stable method to the resolution of the problem. The global stability is a concept of long-time stability and the authors prove that the Runge-Kutta-method for a nonnegative matrix \(D\) is globally stable and asymptotically stable. In the proof of this result new conditions on the sizes \(\alpha\), \(\beta\), \(\gamma\), \(p\) and the choice of the step \(h\) are imposed.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 2137100
zbMATH Keywords: infinite delay-differential equation
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: asymptotic stability
describes a project that uses: RODAS
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
cites work: Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations
cites work: Q4860567
cites work: On the dynamics of a discretized neutral equation
cites work: Stability of the Discretized Pantograph Differential Equation
cites work: Q4839870
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 stability properties of \(\theta\)-methods for the pantograph equation
cites work: Exact and discretized stability of the pantograph equation
cites work: Stability of numerical methods for delay differential equations
cites work: Strong contractivity properties of numerical methods for ordinary and delay differential equations
cites work: Contractivity of Runge-Kutta methods with respect to forcing terms
cites work: Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations
cites work: Stability analysis of Runge-Kutta methods for nonlinear delay differential equations
cites work: Stability and error analysis of one-leg methods for nonlinear delay differential equations
cites work: The discrete dynamics of nonlinear infinite-delay-differential equations
cites work: Non-linear stability of a general class of differential equation methods
cites work: Q4000061
full work available at URL: s0895-7177(04)90520-1
OpenAlex ID: W1992147499
description: scientific article; zbMATH DE number 2137100