Mean-square stability of second-order Runge–Kutta methods for multi-dimensional linear stochastic differential systems

In this paper, the mean-square stability of second-order Runge–Kutta schemes for multi-dimensional linear stochastic differential systems is studied. Motivated by the work of Tocino [Mean-square stability of second-order Runge–Kutta methods for stochastic differential equations, J. Comput. Appl. Math. 175 (2005) 355–367] and Saito and Mitsui [Mean-square stability of numerical schemes for stochastic differential systems, in: International Conference on SCIentific Computation and Differential Equations, July 29–August 3 2001, Vancouver, British Columbia, Canada] we investigate the mean-square stability of second-order Runge–Kutta schemes for multi-dimensional linear stochastic differential systems with one multiplicative noise. Stability criteria are established and numerical examples that confirm the theoretical results are also presented.