Runge-Kutta methods for the numerical solution of stiff semilinear systems
type: Item
instance of: scholarly article
title: Runge-Kutta methods for the numerical solution of stiff semilinear systems
zbMATH Open document ID: 0980.65069
DOI: 10.1023/A:1022332200092
author: Manuel Calvo
author: S. González-Pinto
author: J. I. Montijano
published in: BIT
publication date: 2002-02-25T00:00:00Z
review text: This paper is concerned with the convergence properties of implicit Runge-Kutta methods applied to stiff semilinear systems \[ y'(t) = J(t) y(t) + g(t,y(t)), \] \[ y(0) = y_0 \in R^m, \qquad t \in [0, T] \] with the variable coefficient linear part containing all the stiffness. Two different classes of stiff systems are defined by requiring suitable properties for the relative variation of the matrix \( J(t) \). For each of these classes a family of stable and convergent Runge-Kutta methods which define a unique numerical solution is characterized. As a consequence it is possible to identify Runge-Kutta methods which are not algebraically stable but are suitable for the numerical integration of semilinear problems. The obtained results extend previous ones by \textit{K. Burrage, W. H. Hundsdorfer} and \textit{J. G. Verwer} [Computing 36, 17-34 (1986; Zbl 0572.65053)] on the optimal convergence of implicit Runge-Kutta methods for stiff semilinear systems with constant coefficient linear part.
reviewed by: Riccardo Fazio
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1556485
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: stiff semilinear systems
zbMATH Keywords: stability
zbMATH Keywords: error bounds
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: a:1022332200092
OpenAlex ID: W8805256
description: scientific article; zbMATH DE number 1556485