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2008•arXiv (Cornell University)Open access

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

Xiaohua Ding, Hongyu Liu, Zaijiu Shang, Geng Sun, Lingshu Wang

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Abstract

Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The structure-preservation region provides a practical criterion for choosing step-size in symplectic computation. Examples are given to justify the investigation.

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Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The structure-preservation region provides a practical criterion for choosing step-size in symplectic computation. Examples are given to justify the investigation.

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Available abstract

Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The structure-preservation region provides a practical criterion for choosing step-size in symplectic computation. Examples are given to justify the investigation.

Key concepts: Symplectic geometry, Hamiltonian system, Integrator, Symplectic integrator, Mathematics, Fixed point, Hamiltonian (control theory), Stability (learning theory)

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