Preservation of stability properties near fixed points of linear Hamiltonian systems by symplectic integrators

DOI10.1016/j.amc.2010.12.088zbMath1211.65161arXiv0802.2121OpenAlexW2064282017MaRDI QIDQ632828

Geng Sun, Zaijiu Shang, Hongyu Liu, Xiao-Hua Ding

Publication date: 28 March 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.2121

zbMATH Keywords

stabilitynumerical exampleslinear Hamiltonian systemsstep-size controlequilibrium structurecomposition methodstructure-preservationsymplectic partitioned Runge-Kutta methodsymplectic Runge-Kutta method

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (2)

Numerical Dynamics of Nonstandard Finite Difference Method for Nonlinear Delay Differential Equation ⋮ Symplectic partitioned Runge-Kutta methods with the phase-lag property

Cites Work

• Spurious behavior of a symplectic integrator
• On the nonlinear stability of symplectic integrators
• New aspects in the theory of stability of Hamiltonian systems
• Symmetric Multistip Methods for Periodic Initial Value Problems
• On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods
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