Runge–Kutta methods for Stratonovich stochastic differential equation systems with commutative noise

Abstract

A class of explicit stochastic Runge–Kutta (SRK) methods for Stratonovich stochastic differential equation systems w.r.t. m-dimensional Wiener processes satisfying a commutativity condition is developed. General conditions for the coefficients of the SRK method assuring convergence with order two in the weak sense are presented. Due to the commutativity condition, no correlated random variables have to be generated for the considered Runge–Kutta methods.