标题： 哈密顿方程分裂方法的系统改进 显示英文标题

标题： Systematic Improvement of Splitting Methods for the Hamilton Equations

摘要： 我们展示如何以系统的方式改进哈密顿力学微分方程的标准（Störmer-Verlet）分裂方法（对于步长为$\tau$的时间步，精度为$\tau^2$阶），而无需使用组合方法。我们给出了将精度提高到$\tau^8$阶的显式表达式，并证明该方法在简单的非谐振子上有效。 显示英文摘要

摘要： We show how the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics (with accuracy of order $\tau^2$ for a timestep of length $\tau$) can be improved in a systematic manner without using the composition method. We give the explicit expressions which increase the accuracy to order $\tau^8$, and demonstrate that the method work on a simple anharmonic oscillator.