北京航空航天大学学报 ›› 2013, Vol. ›› Issue (1): 22-26.

• 论文 • 上一篇    下一篇

辛算法的纠飘研究

刘晓梅1, 周钢2, 王永泓1, 孙薇荣2   

  1. 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
  • 收稿日期:2011-10-21 出版日期:2013-01-31 发布日期:2013-01-30
  • 基金资助:
    国家自然科学基金资助项目(50876066)

Rectifying drifts of symplectic algorithm

Liu Xiaomei1, Zhou Gang2, Wang Yonghong1, Sun Weirong2   

  1. 1. School of Mechanical and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
    2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2011-10-21 Online:2013-01-31 Published:2013-01-30

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.

Abstract: Symplectic algorithm preserves the symplectic structure and laws for Hamiltonian systems compared with Runge-Kutta(RK) methods, but the point-wise numerical precision is worse for elliptic Hamiltonian 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.

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