| 辛算法的纠飘研究 |
| |
| 引用本文： | 刘晓梅,周钢,王永泓,孙薇荣.辛算法的纠飘研究[J].北京航空航天大学学报,2013,0(1):22-26. |
| |
| 作者姓名： | 刘晓梅 周钢 王永泓 孙薇荣 |
| |
| 作者单位： | 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 |
| |
| 基金项目： | 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.
|
| 关 键 词： | 辛算法 Runge-Kutta法 相位漂移 哈密顿函数 |
| 收稿时间： | 2011-10-21 |
Rectifying drifts of symplectic algorithm |
| |
| Liu Xiaomei,Zhou Gang,Wang Yonghong,Sun Weirong.Rectifying drifts of symplectic algorithm[J].Journal of Beijing University of Aeronautics and Astronautics,2013,0(1):22-26. |
| |
| Authors: | Liu Xiaomei Zhou Gang Wang Yonghong Sun Weirong |
| |
| Institution: | 1. School of Mechanical and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China |
| |
| 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. |
| |
| Keywords: | symplectic Runge-Kutta methods phase shift Hamiltonian functions |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《北京航空航天大学学报》浏览原始摘要信息 |
| 点击此处可从《北京航空航天大学学报》下载免费的PDF全文 |
|
