Variable step size does not harm second-order integrators for Hamiltonian systems
type: Item
instance of: scholarly article
title: Variable step size does not harm second-order integrators for Hamiltonian systems
zbMATH Open document ID: 0802.65086
DOI: 10.1016/0377-0427(93)90009-Z
published in: Journal of Computational and Applied Mathematics
publication date: 1993-10-10T00:00:00Z
review text: The author describes a number of experiments that have been performed with symplectic integrators for the two-body problem. It is shown that the variable stepsize symplectic integrators do not in general give rise to quadratic growth of the error, i.e. the variable stepsize does not degrade the performance of second-order symplectic integrators. The same refers to variable stepsize nonsymplectic methods. This conclusion is opposed to a report of \textit{M. P. Calvo} and \textit{J. M. Sanz-Serna} [Report 1991/3, Appl. Math. Comput., Univ. Valladolid (1991)] in which the authors indicate that for explicit symplectic integrator applied to the two-body problem, fixed stepsize gives a linear growth of the error, while nonsymplectic and variable stepsize symplectic integrators force the error to grow quadratically.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 70F05
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 81S10
zbMATH DE Number: 428541
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: symplectic integrators
zbMATH Keywords: two-body problem
zbMATH Keywords: variable step size
zbMATH Keywords: performance
author: Daniel Okunbor
reviewed by: Andrzej Marciniak
MaRDI profile type: Publication
cites work: Q4288939
cites work: Symplectic integrators for long-term integrations in celestial mechanics
cites work: Explicit Canonical Methods for Hamiltonian Systems
description: scientific article; zbMATH DE number 428541