Several fourth-order force gradient symplectic algorithms  

作　　者：Jia Xu Xin Wu 

机构地区：[1]Department of Physics, Nanchang University, Nanchang 330031, China

出　　处：《Research in Astronomy and Astrophysics》2010年第2期173-188,共16页天文和天体物理学研究（英文版）

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

摘　　要：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.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.

关 键 词：celestial mechanics -- methods： numerical 

分 类 号：O175.8[理学—数学] TP183[理学—基础数学]