Geometric integration of conservative polynomial ODEs
type: Item
instance of: scholarly article
title: Geometric integration of conservative polynomial ODEs
zbMATH Open document ID: 1021.65064
DOI: 10.1016/S0168-9274(03)00022-9
published in: Applied Numerical Mathematics
publication date: 2003-06-17T00:00:00Z
review text: The authors are concerned with classical Hamiltonian systems where the potential is either cubic or quartic with no cubic terms. For most of these systems they consider explicit numerical integration methods which preserve both phase space volume and the energy. Some applications refer to Henon-Heiles system and hybrid Monte Carlo method. No numerical results are included.
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 37M15
zbMATH DE Number: 1929428
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: cubic and quartic potentials
zbMATH Keywords: explicit integration methods
zbMATH Keywords: splitting
zbMATH Keywords: composition
zbMATH Keywords: phase space volume preservation
zbMATH Keywords: energy preservation
zbMATH Keywords: Henon-Heiles systems
zbMATH Keywords: hybrid Monte-Carlo method
author: Robert I. McLachlan
author: G. R. W. Quispel
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
cites work: Stability of Runge-Kutta Methods for Trajectory Problems
cites work: Six lectures on the geometric integration of ODEs
cites work: Generating functions for dynamical systems with symmetries, integrals, and differential invariants
cites work: Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals
cites work: Equivariant constrained symplectic integration
cites work: On the discretization of the three-dimensional Volterra system
cites work: Construction of higher order symplectic schemes by composition
cites work: The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics
cites work: Q4941180
full work available at URL: s0168-9274(03)00022-9
OpenAlex ID: W2075546756
Recommended article: Geometric integrators for ODEs
Recommended article: Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables
Recommended article: Geometry of polynomial ordinary differential equations
Recommended article: Explicit geometric integration of polynomial vector fields
Recommended article: Integration of PDEs by differential geometric means
Recommended article: The geometric integration of scale-invariant ordinary and partial differential equations
Recommended article: Q4531870
Recommended article: Geometric Numerical Integration
Recommended article: Geometric integration methods that preserve Lyapunov functions
description: scientific article; zbMATH DE number 1929428