High-order Runge-Kutta-Nyström geometric methods with processing

DOI10.1016/S0168-9274(00)00035-0zbMath0990.65137OpenAlexW2061640517MaRDI QIDQ5954977

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Publication date: 7 February 2002

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

Full work available at URL: https://doi.org/10.1016/s0168-9274(00)00035-0

zbMATH Keywords

Lie algebrainitial value problemsflowsgeometric integrationprocessing techniqueRunge-Kutta-Nyström geometric methods

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Periodic orbits of vector fields and flows (37C27) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (6)

On the linear stability of splitting methods ⋮ High order numerical integrators for differential equations using composition and processing of low order methods ⋮ Splitting and composition methods for explicit time dependence in separable dynamical systems ⋮ Raising the order of geometric numerical integrators by composition and extrapolation ⋮ The Lie algebra of classical mechanics ⋮ Runge-Kutta-Nyström symplectic splitting methods of order 8

Cites Work

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• A symplectic integration algorithm for separable Hamiltonian functions
• A numerical algorithm for Hamiltonian systems
• Canonical Runge-Kutta-Nyström methods of orders five and six
• Explicit Symplectic Integrators Using Hessian--Vector Products
• Algorithm 670: a Runge-Kutta-Nyström code
• High-Order Symplectic Runge–Kutta–Nyström Methods
• On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods
• Symplectic Integration with Processing: A General Study

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