A class of second-order Runge-Kutta methods for numerical solution of stochastic differential equations

Abstract

A class of explicit Runge-Kutta methods for numerical solution of stochastic differential equations is described, analyzed, and numerically tested. It is shown that this class is of second-order accuracy in the weak sense. Also, a varaince reduction technique is presented that reduces the stochastic error involved when computing expectations. Numerical examples are presented to support the theoretical results.