On the nonlinear stability of symplectic integrators
type: Item
instance of: scholarly article
title: On the nonlinear stability of symplectic integrators
zbMATH Open document ID: 1070.65130
author: M. Perlmutter
author: Robert I. McLachlan
author: G. R. W. Quispel
published in: BIT
publication date: 2004-08-06T00:00:00Z
review text: The paper deals mainly with the problem of achieving stability for symplectic numerical integrators by the mean of studying the topological equivalence of the level sets of the original Hamiltonian and those of the modified Hamiltonian associated to the numerical integrators. Using Morse theory, the authors gives criteria to detemine topological stability for integrators (in particular, there are results for Runge-Kutta and splitting methods). For non-degenerate Hamiltonians, `nonlinear stability' for integrators is defined and a simple (once given the modified Hamiltonian) analytical criterion for stability is stated. The criterion is used on Runge-Kutta and splitting algorithms for mechanical systems in one and two degree of freedom.
reviewed by: Anna Maria Cherubini
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 65P40
Mathematics Subject Classification ID: 58K05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 37J25
zbMATH DE Number: 2081531
zbMATH Keywords: symplectic integration
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: backward error analysis
zbMATH Keywords: Hamiltonian
zbMATH Keywords: splitting methods
zbMATH Keywords: nonlinear stability
MaRDI profile type: Publication
full work available at URL: b:bitn.0000025088.13092.7f
OpenAlex ID: W2099535332
DOI: 10.1023/B:BITN.0000025088.13092.7F
description: scientific article; zbMATH DE number 2081531