Improved high order integrators based on the Magnus expansion
type: Item
instance of: scholarly article
title: Improved high order integrators based on the Magnus expansion
zbMATH Open document ID: 0962.65102
DOI: 10.1023/A:1022311628317
author: R. Smith
published in: BIT
publication date: 2001-06-14T00:00:00Z
review text: This paper presents high-order efficient numerical integration methods for solving the initial value problem defined by the linear differential equation \[ \dot X= A(t)X,\qquad X(t_0)=\dot I, \] based on the Magnus expansion. These methods preserve intrinsic geometric properties of the exact solution. New approximation schemes of order four, six and eight to the Magnus expansion involving exclusively single analytical integrals with just one, four and ten commutators, respectively, are obtained. Sixth- and eight-order numerical algorithms with automatic step-size control are constructed explicitly. The theory of free Lie algebra is used.
reviewed by: Laura Iulia Aniţa
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 1533016
zbMATH Keywords: error bounds
zbMATH Keywords: initial value problem
zbMATH Keywords: linear differential equation
zbMATH Keywords: Magnus expansion
zbMATH Keywords: algorithms
zbMATH Keywords: automatic step-size control
zbMATH Keywords: free Lie algebra
MaRDI profile type: Publication
full work available at URL: a:1022311628317
OpenAlex ID: W1608348832
description: scientific article; zbMATH DE number 1533016