Runge-Kutta methods for monotone differential and delay equations
type: Item
instance of: scholarly article
title: Runge-Kutta methods for monotone differential and delay equations
zbMATH Open document ID: 1048.65073
DOI: 10.1023/B:BITN.0000007059.99601.18
author: Johannes Schropp
author: Peter E. Kloeden
published in: BIT
publication date: 2004-06-11T00:00:00Z
review text: The authors present classes of Runge-Kutta methods for nonlinear ordinary and delay differential equations for which the numerical dynamical system shares the monotonicity behaviour of the continuous time system. A Runge-Kutta method is given by the weight vector and the coefficient matrix \(A\). The positivity of the weights and the nonnegativity of the components of the matrix \((I+\tau A)^{-1}A\) for sufficiently small \(\tau>0\) ensure that the monotonicity is preserved.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34K28
zbMATH DE Number: 2073452
zbMATH Keywords: monotone dynamical systems
zbMATH Keywords: delay equations
zbMATH Keywords: Runge-Kutta methods
reviewed by: Rudolf Scherer
MaRDI profile type: Publication
full work available at URL: b:bitn.0000007059.99601.18
OpenAlex ID: W2031279116
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description: scientific article; zbMATH DE number 2073452