摘要
In this paper, the linear stability of symplectic methods for Hamiltonian systems is studied. In par- ticular, three classes of symplectic methods are considered： symplectic Runge-Kutta （SRK） methods, symplectic partitioned Runge-Kutta （SPRK） methods and the composition methods based on SRK or SPRK methods. It is shown that the SRK methods and their compositions preserve the ellipticity of equilibrium points uncondi- tionally, whereas the SPRK methods and their compositions have some restrictions on the time-step.
In this paper, the linear stability of symplectic methods for Hamiltonian systems is studied. In par- ticular, three classes of symplectic methods are considered： symplectic Runge-Kutta （SRK） methods, symplectic partitioned Runge-Kutta （SPRK） methods and the composition methods based on SRK or SPRK methods. It is shown that the SRK methods and their compositions preserve the ellipticity of equilibrium points uncondi- tionally, whereas the SPRK methods and their compositions have some restrictions on the time-step.
基金
Supported by the National Natural Science Foundation of China (No. 10926064,10571173)
the Scientific Research Foundation of Hebei Education Department (No. 2009114)
