精细辛几何算法的误差估计

Accuracy Estimation of Precise Symplectic Integration Method

该文讨论了精细辛几何算法的计算误差,先展开二阶和四阶精细辛几何算法的表达式得到误差同精细剖分数目的关系,然后分析了任意阶精细辛几何算法的误差,得到了一致简洁的结果,总的误差可近似表示为单个精细步长的误差乘以剖分数目,最后讨论了在要求控制精度下剖分数目的选取,该方法克服了算法精度对积分时间步长的依赖性．

In this paper the calculation accuracy of precise symplectic integration method is discussed. At first, the two and four degree accuracy algorithms are analyzed and the relation of the error to the value of the precise integration number is obtained. Then, the accuracy of any degree precise symplectic algorithm is also discussed and the obtained result is the same and simple. The total error of the method can be approximately written in the calculation error of one time step multiplied by the integration number. Finally, the appropriate integration number is estimated at the control accuracy. It can be found that by this method the accuracy of precise symplectic integration will no longer be controlled by the value of the time step.