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. (C) 2007 Elsevier B.V. All rights reserved.