Three-Stage Stiffly Accurate Runge-Kutta Methods for Stiff Stochastic Differential Equations (Communications in Mathematical Research, 2021)
In this paper we discuss diagonally implicit and semi-implicit methodsbased 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 truncatedrandom variable is used in the implicit method. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation ofstiff SDEs.
Keywords: stochastic differential equation; Runge-Kutta method; stability; stiff accuracy.