Mean-square stability of second-order Runge–Kutta methods for stochastic differential equations

In a previous paper, we proposed the stochastic generalization of classical second-order two-stage explicit Runge–Kutta (RK) methods. The obtained stochastic schemes have second order in the weak sense. In this paper, the numerical stability of these RK schemes is studied. The study focuses on stability with respect to the second moment (MS-stability). Figures of the stability domains of the numerical schemes are shown. Numerical examples that confirm the theoretical results are also presented.