Composite integrators for bi-Hamiltonian systems
type: Item
instance of: scholarly article
title: Composite integrators for bi-Hamiltonian systems
zbMATH Open document ID: 0873.58033
DOI: 10.1016/0898-1221(96)00157-5
publication date: 1997-09-28T00:00:00Z
review text: There is a great interest to construct numerical algorithms for dynamical systems preserving geometric structure. The authors apply symmetric explicit composite integrators of different order to some three-dimensional bi-Hamiltonian systems which are time-reversible, source-free, and have periodic solutions; such as Lotka-Volterra equations, the conservative Lorenz system, and the periodic Toda lattice. The numerical results obtained show that the Hamiltonians are preserved with high accuracy and the periodicity of the solutions is retained.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 980331
zbMATH Keywords: Lotka-Volterra equations
zbMATH Keywords: Toda lattice
zbMATH Keywords: periodicity
zbMATH Keywords: solutions
zbMATH Keywords: Lorenz equation
zbMATH Keywords: bi-Hamiltonian structure
zbMATH Keywords: symmetric composite integrators
author: Bülent Karasözen
reviewed by: G.V.Khmelevskaja-Plotnikova
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00157-5
OpenAlex ID: W1977770641
cites work: On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods
cites work: Convergence of general decompositions of exponential operators
cites work: Poisson structure of dynamical systems with three degrees of freedom
cites work: Q4273954
cites work: Fourth-order symplectic integration
cites work: Quantum Monte Carlo methods and general decomposition theory of exponential operators and symplectic integrators
cites work: Bi-Hamiltonian structure of the \(qd\) algorithm and new discretizations of the Toda lattice
cites work: Energy superconvergence of one-step methods for separable Hamiltonian systems
cites work: On the discretization of the three-dimensional Volterra system
cites work: Volume-preserving algorithms for source-free dynamical systems
cites work: Volume-preserving integrators
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 980331