Runge-Kutta methods for linear ordinary differential equations
type: Item
instance of: scholarly article
title: Runge-Kutta methods for linear ordinary differential equations
zbMATH Open document ID: 0935.65077
DOI: 10.1016/S0168-9274(98)00129-9
published in: Applied Numerical Mathematics
publication date: 2000-04-24T00:00:00Z
review text: Spatial discretizations of linear partial differential equations lead to systems of ordinary differential equations of the form \(u'=Au-g(t)\). This motivates the authors to construct new explicit \(4\)-, \(5\)-, and \(6\)-stage Runge-Kutta methods, which are \(3\)rd order accurate for nonlinear problems, but for problems of the form \(u'=Au-g(t)\) they are of order \(4\), \(5\), and \(6\), respectively. The stability polynomials of the new methods coincide with the truncated Taylor series of \(\exp z\).
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1367742
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: linear differential equations
zbMATH Keywords: method of lines
zbMATH Keywords: systems
zbMATH Keywords: stability
author: D. W. Zingg
author: Todd T. Chisholm
MaRDI profile type: Publication
full work available at URL: s0168-9274(98)00129-9
OpenAlex ID: W2010379067
description: scientific article; zbMATH DE number 1367742