Symplectic algebraic dynamics algorithm  

作　　者：WANG ShunJin ZHANG Hua 

机构地区：[1]Center of Theoretical Physics,Sichuan University,Chengdu 610064,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2007年第2期133-143,共11页中国科学：物理学、力学、天文学（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.10375039 and 90503008);the Doctoral Program Foundation of the Ministry of Education of China,and the Center of Nuclear Physics of HIRFL of China

摘　　要：Based on the algebraic dynamics solution of ordinary differential equations and integration of $\hat L$ , the symplectic algebraic dynamics algorithm s? n is designed, which preserves the local symplectic geometric structure of a Hamiltonian system and possesses the same precision of the na?ve algebraic dynamics algorithm ? n . Computer experiments for the 4th order algorithms are made for five test models and the numerical results are compared with the conventional symplectic geometric algorithm, indicating that s? n has higher precision, the algorithm-induced phase shift of the conventional symplectic geometric algorithm can be reduced, and the dynamical fidelity can be improved by one order of magnitude.Based on the algebraic dynamics solution of ordinary differential equations andintegration of ,the symplectic algebraic dynamics algorithm sn is designed,which preserves the local symplectic geometric structure of a Hamiltonian systemand possesses the same precision of the na ve algebraic dynamics algorithm n.Computer experiments for the 4th order algorithms are made for five test modelsand the numerical results are compared with the conventional symplectic geometric algorithm,indicating that sn has higher precision,the algorithm-inducedphase shift of the conventional symplectic geometric algorithm can be reduced,and the dynamical fidelity can be improved by one order of magnitude.

关 键 词：SYMPLECTIC ALGEBRAIC dynamics ALGORITHM PRESERVING local SYMPLECTIC geometric structure reduction of algo-rithm-induced phase shift improving DYNAMICAL FIDELITY 

分 类 号：O175[理学—数学]