A technique to improve the error propagation when integrating relative equilibria
type: Item
instance of: scholarly article
title: A technique to improve the error propagation when integrating relative equilibria
zbMATH Open document ID: 1071.65173
DOI: 10.1023/B:BITN.0000039391.19365.56
published in: BIT
publication date: 2005-04-07T00:00:00Z
review text: The aim of the paper is the study of a way to improve the propagation errors in the numerical integration of relative equilibria solution of Hamiltonian differential equations with symmetries. One knows that in this case and for stable equilibria, the error growth is typically quadratic for ``general'' schemes and linear for schemes that preserve the invariant quantities of the problem. The first part is an introduction concerning the existing studies and the analysed cases. The second part summarizes basic results about Hamiltonian relative equilibrium problems. The authors consider one parameter symmetry groups. They give also an example considering a Hamiltonian problem with four degrees of freedom. The third part presents the numerical problem and the study of the linearization around the relative equilibrium which is necessary to understand the error propagation. From this, the technique of modification is introduced, its implementation is discussed and the asymptotic behaviour of the new methods in the numerical integration of Hamiltonian relative equilibria is stated. The fourth part contains numerical examples, including small perturbations of the relative equilibrium, in order to illustrate the above technique and the gain in efficiency it implies.
reviewed by: Romulus Militaru
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 37C80
Mathematics Subject Classification ID: 37D35
zbMATH DE Number: 2153699
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: symmetries of differential equations
zbMATH Keywords: relative equilibria
zbMATH Keywords: error propagation
zbMATH Keywords: conservative numerical methods
zbMATH Keywords: numerical examples
author: Begoña Cano
author: A. Durán
MaRDI profile type: Publication
full work available at URL: b:bitn.0000039391.19365.56
OpenAlex ID: W1984046815
description: scientific article; zbMATH DE number 2153699