Characterizations and construction of Poisson/symplectic and symmetric multi-revolution implicit Runge-Kutta methods of high order

DOI10.1016/j.apnum.2007.04.001zbMath1149.65096OpenAlexW2071789734MaRDI QIDQ928845

Min Li, Ai-Guo Xiao

Publication date: 11 June 2008

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2007.04.001

zbMATH Keywords

symplectic methodsGauss type methodLobatto type methodmodified W-transformationmulti-revolution Runge-Kutta methodsnear identity mapPoisson type methodRadau type method

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

Constructive characterization of Runge-Kutta methods that satisfy the M-condition

Uses Software

• RODAS

Cites Work

• A new approach to the construction of multirevolution methods and their implementation
• On symmetric Runge-Kutta methods of high order
• On explicit multi-revolution Runge-Kutta schemes
• On ODE-solver based on the method of averaging
• Perturbed collocation and Runge-Kutta methods
• A generalized \(W\)-transformation for constructing symplectic partitioned Runge-Kutta methods
• Symplectic properties of multistep Runge-Kutta methods.
• Order properties of symplectic Runge-Kutta-Nyström methods
• Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods
• Algebraically Stable and Implementable Runge-Kutta Methods of High Order
• An Efficient Numerical Method for Highly Oscillatory Ordinary Differential Equations
• Modified multirevolution integration methods for satellite orbit computation
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