On the implementation of the method of Magnus series for linear differential equations
type: Item
instance of: scholarly article
title: On the implementation of the method of Magnus series for linear differential equations
zbMATH Open document ID: 0933.65077
DOI: 10.1023/A:1022393913721
author: Arieh Iserles
author: Arne Marthinsen
author: Syvert P. Nørsett
published in: BIT
publication date: 2000-04-04T00:00:00Z
review text: This paper first reviews the solution of the matrix equation \(y'(H)= A(t)y(t)\) by the use of the Magnus expansion. Here the solution is written in the form \(y(t)= \exp(\Omega(H))y_0\), where \(\Omega\) is an infinite expansion of iterated commutators of the integrals of \(A(t)\), via a rooted tree theory approach. The authors then consider the error behaviour when this expansion is truncated and also give a two stage, fourth-order numerical method based on the evaluation of \(A\) at the Gaussian quadrature points. Some numerical results, but only for linear problems, are presented.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 1309454
zbMATH Keywords: method of Magnus series
zbMATH Keywords: Lie groups
zbMATH Keywords: numerical examples
zbMATH Keywords: systems
zbMATH Keywords: error bounds
reviewed by: Kevin Burrage
MaRDI profile type: Publication
full work available at URL: a:1022393913721
OpenAlex ID: W1584723409
description: scientific article; zbMATH DE number 1309454