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

TL;DR

This paper investigates how symplectic integrators, specifically SRK and SPRK methods, preserve stability structures near fixed points in linear Hamiltonian systems, providing practical criteria for step-size selection.

Contribution

It introduces structure-preservation regions for symplectic methods applied to linear Hamiltonian systems, aiding in effective step-size choice and stability preservation.

Findings

Structure-preservation regions are identified for symplectic integrators.

Practical criteria for step-size selection are proposed.

Examples demonstrate the effectiveness of the methods.

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.