Three-Stage Stiffly Accurate Runge-Kutta Methods for Stiff Stochastic Differential Equations

Abstract

In this paper we discuss diagonally implicit and semi-implicit methods based on the three-stage stiffly accurate Runge-Kutta methods for solving Stratonovich stochastic differential equations (SDEs). Two methods, a three-stage stiffly accurate semi-implicit (SASI3) method and a three-stage stiffly accurate diagonally implicit (SADI3) method, are constructed in this paper. In particular, the truncated random variable is used in the implicit method. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of stiff SDEs.