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

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 effectivenes...