On the conservativeness of two-stage symmetric-symplectic Runge-Kutta methods and the Störmer-Verlet method

DOI10.1134/S0012266110070062zbMath1204.65143OpenAlexW1965592573MaRDI QIDQ610383

G. G. Elenin, P. I. Shlyakhov

Publication date: 8 December 2010

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266110070062

zbMATH Keywords

algorithmCauchy problemnumerical examplesmolecular dynamicsHamiltonian equationStörmer-Verlet methodsymplectic Runge-Kutta methodssymplectic and symmetric methods

Mathematics Subject Classification ID

Hamilton's equations (70H05) 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 (2)

Testing a new conservative method for solving the Cauchy problem for Hamiltonian systems on test problems ⋮ On the conservativeness of a two-parameter family of three-stage symmetric-symplectic Runge-Kutta methods

Cites Work

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• Runge-Kutta schemes for Hamiltonian systems
• Conservative numerical methods for \(\ddot x=f(x)\)
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
• Simulating Hamiltonian Dynamics
• Symplectic-energy-momentum preserving variational integrators
• Sympletic Runge--Kutta Shemes I: Order Conditions
• Geometric numerical integration illustrated by the Störmer–Verlet method
• Geometric Numerical Integration

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