Stochastic Runge-Kutta algorithms. I. White noise

A higher-order algorithm for the numerical integration of one-variable, additive, white-noise equations is developed. The method of development is to extend standard deterministic Runge-Kutta algorithms to include stochastic terms. The ability of the algorithm to generate proper correlation properties is tested on the Ornstein-Uhlenbeck process, showing higher accuracy even with longer step size.