Further reduction in the number of independent order conditions for symplectic, explicit partitioned Runge-Kutta and Runge-Kutta-Nyström methods

DOI10.1016/0168-9274(95)00047-XzbMath0885.65087OpenAlexW2013246605MaRDI QIDQ1902067

M. P. Calvo, Ernst Hairer

Publication date: 2 April 1998

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

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00047-x

zbMATH Keywords

Runge-Kutta-Nyström methodsHamiltonian systemorder conditionssymplecticpartitioned symplectic Runge-Kutta methodsfree Lie algebra theory

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Dynamical systems and ergodic theory (37-XX)

Related Items

Partitioned general linear methods for separable Hamiltonian problems, Explicit symplectic partitioned Runge-Kutta-Nyström methods for non-autonomous dynamics, Order properties of symplectic Runge-Kutta-Nyström methods, Partitioned second derivative methods for separable Hamiltonian problems, A SYMPLECTIC ALGORITHM FOR THE STABILITY ANALYSIS OF NONLINEAR PARAMETRIC EXCITED SYSTEMS

Cites Work

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• Order conditions for canonical Runge-Kutta-Nyström methods
• The Development of Variable-Step Symplectic Integrators, with Application to the Two-Body Problem
• Solving Ordinary Differential Equations I
• Explicit Canonical Methods for Hamiltonian Systems
• On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods
• Partitioned Runge-Kutta Methods for Separable Hamiltonian Problems