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In a previous paper, a method was presented to integrate numerically nonlinear stochastic differential equations (SDEs) with additive, Gaussian, white noise. The method, a generalization of the Range Kutta algorithm, extrapolates from one point to the next applying functional evaluations at stochastically determined points. This paper extends (and at one point corrects) algorithms for the simple class of equations considered in the previous paper. In addition, the method is expanded to treat vector SDEs, equations with time-dependent functions, and SDEs higher than first order. The parameters for several explicit integration schemes are displayed.
Greenside et al. (Thu,) studied this question.