Using simplifying assumptions that are related to the time reversal symmetry, a 1-dimensional family of 8-stage pseudo-symplectic Runge-Kutta methods of order (4, 8), i.e., methods of order 4 that preserve symplectic structure up to order 8, is derived. An example of 7-stage method of order (4, 9) is given.

翻译：利用与时间反演对称性相关的简化假设，推导出一维八级伪辛龙格-库塔方法的(4,8)阶格式族（即阶数为4且辛结构保持至8阶的方法）。文中还给出了一个(4,9)阶七级方法的算例。