Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations
type: Item
instance of: scholarly article
title: Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations
zbMATH Open document ID: 0904.65082
DOI: 10.1016/S0377-0427(97)00118-0
published in: Journal of Computational and Applied Mathematics
publication date: 1999-01-19T00:00:00Z
review text: Stability and convergence of Runge-Kutta methods with Lagrangian interpolation applied to nonlinear ordinary delay differential equations are studied. The new concepts of strong algebraic stability, GDN-stability and D-convergence are introduced to facilitate the analysis. A correspondence between certain stability properties of Runge-Kutta methods applied to ordinary differential equations and relevant stability properties of the same methods enhanced by Lagrangian interpolation and applied to delay differential equations is established.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 1100611
zbMATH Keywords: nonlinear stability
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: delay differential equations
zbMATH Keywords: strong algebraic stability
zbMATH Keywords: GDN-stability
zbMATH Keywords: D-convergence
author: Cheng-Jian Zhang
author: Shuzi Zhou
reviewed by: Nikolai L. Vulchanov
MaRDI profile type: Publication
cites work: Q4030650
cites work: Strong contractivity properties of numerical methods for ordinary and delay differential equations
cites work: High order algebraically stable Runge-Kutta methods
cites work: Stability Criteria for Implicit Runge–Kutta Methods
cites work: G-stability is equivalent toA-stability
cites work: Q3687624
cites work: The automatic integration of ordinary differential equations
cites work: Q5719651
cites work: A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
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: One-Step Methods of any Order for Neutral Functional Differential Equations
cites work: Stability of numerical methods for delay differential equations
cites work: P-stability properties of Runge-Kutta methods for delay differential equations
full work available at URL: s0377-0427(97)00118-0
OpenAlex ID: W2010390180
description: scientific article; zbMATH DE number 1100611