Fer's factorization as a symplectic integrator
type: Item
instance of: scholarly article
title: Fer's factorization as a symplectic integrator
zbMATH Open document ID: 0862.65042
author: Fernando Casas
published in: Numerische Mathematik
publication date: 1997-05-25T00:00:00Z
review text: The author presents the Fer expansion as a possible explicit symplectic integrator for time-dependent Hamiltonian systems. When this iterative procedure is applied to an arbitrary Hamiltonian, a factorization of the time-evolution map is obtained as an infinite product of Lie transformations. The author shows that, at least for quadratic Hamiltonians, very few iterations are sufficient to achieve accurate results both for the orbits and conserved quantities. Numerical experiments presented in this paper show the performance of the proposed method. The third- and fourth-order Fer expansions are compared with other numerical integration schemes, including symplectic ones. It appears that the performance of the Fer factorization is comparable to that of the Gragg-Bulirsch-Stoer extrapolation algorithm, and it is better than other symplectic integration methods such as the explicit Runge-Kutta-Nyström and Gauss-Legendre Runge-Kutta algorithms.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 932030
zbMATH Keywords: Runge-Kutta-Nyström algorithm
zbMATH Keywords: numerical experiments
zbMATH Keywords: Fer expansion
zbMATH Keywords: symplectic integrator
zbMATH Keywords: time-dependent Hamiltonian systems
zbMATH Keywords: performance
zbMATH Keywords: Gragg-Bulirsch-Stoer extrapolation algorithm
zbMATH Keywords: Gauss-Legendre Runge-Kutta algorithms
reviewed by: Andrzej Marciniak
MaRDI profile type: Publication
full work available at URL: s002110050217
OpenAlex ID: W2066685248
DOI: 10.1007/S002110050217
description: scientific article; zbMATH DE number 932030