Stiffly accurate Runge–Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge–Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge–Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs