A stochastic method for all seasons

It is well known that the numerical solution of stochastic ordinary differential equations leads to a step size reduction when explicit methods are used. This has led to a plethora of implicit methods with a wide variety of stability properties. However, for stochastic problems whose eigenvalues lie near the negative real axis, explicit methods with extended stability regions can be very effective. In this paper we extend these ideas to the stochastic realm and present a family of weak order two explicit stochastic Runge-Kutta methods with extended stability intervals that can be used to solve a variety of non-stiff and stiff problems.