By adding force gradient operators to symmetric compositions, we build a set of explicit fourth-order force gradient symplectic algorithms, including those of Chin and coworkers, for a separable Hamiltonian system wit...By adding force gradient operators to symmetric compositions, we build a set of explicit fourth-order force gradient symplectic algorithms, including those of Chin and coworkers, for a separable Hamiltonian system with quadratic kinetic en- ergy T and potential energy V. They are extended to solve a gravitational n-body Hamiltonian system that can be split into a Keplerian part H0 and a perturbation part H1 in Jacobi coordinates. It is found that the accuracy of each gradient scheme is greatly superior to that of the standard fourth-order Forest-Ruth symplectic integra- tor in T ＋ V-type Hamiltonian decomposition, but they are both almost equivalent in the mean longitude and the relative position for H0 ＋//1-type decomposition. At the same time, there are no typical differences between the numerical performances of these gradient algorithms, either in the splitting of T ＋ V or in the splitting of H0 ＋//1. In particular, compared with the former decomposition, the latter can dra- matically improve the numerical accuracy. Because this extension provides a fast and high-precision method to simulate various orbital motions of n-body problems, it is worth recommending for practical computation.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10873007)supported by the Science Foundation of Jiangxi Education Bureau (GJJ09072)Program for Innovative Research Team of Nanchang University
文摘By adding force gradient operators to symmetric compositions, we build a set of explicit fourth-order force gradient symplectic algorithms, including those of Chin and coworkers, for a separable Hamiltonian system with quadratic kinetic en- ergy T and potential energy V. They are extended to solve a gravitational n-body Hamiltonian system that can be split into a Keplerian part H0 and a perturbation part H1 in Jacobi coordinates. It is found that the accuracy of each gradient scheme is greatly superior to that of the standard fourth-order Forest-Ruth symplectic integra- tor in T ＋ V-type Hamiltonian decomposition, but they are both almost equivalent in the mean longitude and the relative position for H0 ＋//1-type decomposition. At the same time, there are no typical differences between the numerical performances of these gradient algorithms, either in the splitting of T ＋ V or in the splitting of H0 ＋//1. In particular, compared with the former decomposition, the latter can dra- matically improve the numerical accuracy. Because this extension provides a fast and high-precision method to simulate various orbital motions of n-body problems, it is worth recommending for practical computation.
