辛算法的纠飘研究  

Rectifying drifts of symplectic algorithm

作　　者：刘晓梅[1] 周钢[2] 王永泓[1] 孙薇荣[2] 

机构地区：[1]上海交通大学机械与动力学院,上海200240 [2]上海交通大学数学系,上海200240

出　　处：《北京航空航天大学学报》2013年第1期22-26,共5页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国家自然科学基金资助项目(50876066)

摘　　要：辛算法较RK(Runge-Kutta)方法,保持辛结构不变或保持哈密顿系统规律性不变是突出的优点,但点态数值精度并不理想.推导出了三阶、四阶辛算法的漂移量计算公式,通过补偿漂移量就能提高点态数值精度,既保辛结构又保证点态数值高精度,适合于工程应用.建立了分数步对称辛算法(即FSJS算法)的纠漂公式,制定了漂移的约束标准.相关算例的数值结果表明:三阶FSJS算法漂移量最小,点态数值精度更高.Symplectic algorithm preserves the symplectic structure and laws for Hamiltonian systems com- pared with Runge-Kutta（RK） methods, but the point-wise numerical precision is worse for elliptic Hamihoni- an systems. In order to improve it, the average statistic drift formulae of the third-order symplectic method and the fourth-order scheme were deduced. The precision was improved through compensating the drifts and step segmentation. A standard was built to find a better symplectic scheme in phase drift. The results of examples show that the third-order fractional step and symmetric symplectic algorithm（ FSJS3 algorithm） is higher than the fourth-order one in phase accuracy, which is recommended for engineering application.

关 键 词：辛算法 RUNGE-KUTTA法 相位漂移 哈密顿函数 

分 类 号：O241[理学—计算数学] O302[理学—数学]