Lack of dissipativity is not symplecticness

DOI10.1007/BF01737166zbMath0844.65062OpenAlexW2051012697MaRDI QIDQ1899935

Yanyan Li

Publication date: 29 August 1996

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01737166

zbMATH Keywords

Hamiltonian systemsKepler problemsymplectic algorithmfourth-order three stage Runge-Kutta-Nyström algorithmnondissipative algorithm

Mathematics Subject Classification ID

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 (4)

A conservative fourth-order real space method for the (2+1)D Dirac equation ⋮ A high-order explicit Runge-Kutta pair for initial value problems with oscillating solutions ⋮ Relaxation Runge-Kutta methods for Hamiltonian problems ⋮ High-order zero-dissipative Runge-Kutta-Nyström methods

Cites Work

• Variable step size does not harm second-order integrators for Hamiltonian systems
• Order conditions for canonical Runge-Kutta-Nyström methods
• Fourth-order symplectic integration
• A symplectic integration algorithm for separable Hamiltonian functions
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• The Development of Variable-Step Symplectic Integrators, with Application to the Two-Body Problem
• Solving Ordinary Differential Equations I
• The canonicity of mappings generated by Runge-Kutta type methods when integrating the systems
• Some properties of methods for the numerical integration of systems of the form
• The accuracy of symplectic integrators
• An Explicit Runge–Kutta–Nyström Method is Canonical If and Only If Its Adjoint is Explicit
• Explicit Canonical Methods for Hamiltonian Systems
• High-Order Symplectic Runge–Kutta–Nyström Methods
• On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods

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