Geometric integration of conservative polynomial ODEs

DOI10.1016/S0168-9274(03)00022-9zbMath1021.65064OpenAlexW2075546756MaRDI QIDQ1811696

Robert I. Mclachlan, Gilles Reinout Willem Quispel

Publication date: 17 June 2003

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(03)00022-9

zbMATH Keywords

Hamiltonian systemssplittingcompositionenergy preservationHenon-Heiles systemsexplicit integration methodscubic and quartic potentialshybrid Monte-Carlo methodphase space volume preservation

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (5)

NONSTANDARD DISCRETIZATION SCHEMES APPLIED TO THE CONSERVATIVE HÉNON–HEILES SYSTEM ⋮ Connections and Extensions: A Discussion of the Paper by Girolami and Byrne ⋮ Runge-Kutta projection methods with low dispersion and dissipation errors ⋮ Geometric integrators for piecewise smooth Hamiltonian systems ⋮ Energy preserving symplectic integrators

Cites Work

• Generating functions for dynamical systems with symmetries, integrals, and differential invariants
• Construction of higher order symplectic schemes by composition
• The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics
• Equivariant constrained symplectic integration
• On the discretization of the three-dimensional Volterra system
• Stability of Runge-Kutta Methods for Trajectory Problems
• Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals
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