We present an algorithm for the numerical solution of ordinary differential equations by random enumeration of the Butcher trees used in the implementation of the Runge-Kutta method. Our Monte Carlo scheme allows for the direct numerical evaluation of an ODE solution at any given time within a certain interval, without iteration through multiple time steps. In particular, this approach does not involve a discretization step size, and it does not require the truncation of Taylor series.

翻译：我们提出了一个算法,通过随机查点执行龙格-库塔方法中使用的屠夫树,对普通差异方程式进行数字解析。我们的蒙特卡洛计划允许在一定的间隔内,在任何特定时间内对ODE解决方案进行直接的数字评估,而不必通过多次步骤重复。 特别是,这一方法不涉及离散步骤大小,也不要求Taylor系列的脱轨。