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

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.