The cohesiveness of G-symplectic methods

DOI10.1007/s11075-015-9964-yzbMath1330.65192OpenAlexW2094674053MaRDI QIDQ891785

John C. Butcher

Publication date: 17 November 2015

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-015-9964-y

zbMATH Keywords

invarianceCauchy problemcohesivenesssymplectic methodone step methodG-symplectic methodHénon-Heiles probleminternal startingparasitic growthsystem of ODE

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

Related Items (5)

Composite symmetric second derivative general linear methods for Hamiltonian systems ⋮ Runge–Kutta Methods for Ordinary Differential Equations ⋮ G-symplectic second derivative general linear methods for Hamiltonian problems ⋮ Partitioned general linear methods for separable Hamiltonian problems ⋮ Projection of second derivative methods for ordinary differential equations with invariants

Cites Work

• Order conditions for G-symplectic methods
• Multi-step methods are essentially one-step methods
• Runge-Kutta schemes for Hamiltonian systems
• On the Butcher group and general multi-value methods
• General linear methods: Connection to one step methods and invariant curves
• Dealing with Parasitic Behaviour in G-Symplectic Integrators
• The Control of Parasitism in $G$-symplectic Methods
• An Algebraic Theory of Integration Methods
• General linear methods
• Numerical Methods for Ordinary Differential Equations
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