论文标题
通过屠夫系列的蒙特卡洛枚举对ODE溶液的数值评估
Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
论文作者
论文摘要
我们通过随机枚举在Runge-kutta方法实现中使用的屠夫树，为普通微分方程的数值解提供了一种算法。我们的Monte Carlo方案允许在一定时间间隔内的任何给定时间进行直接对ODE解决方案的数值评估，而无需通过多个时间步骤进行迭代。特别是，这种方法不涉及离散的步长大小，并且不需要泰勒系列的截断。
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.
