  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.
