Multi-dimensional linear stability analysis of S-ROCK methods for Itô stochastic differential equations

In this paper, stochastic orthogonal Runge-Kutta Chebyshev methods are dealt with for strong approximations to solutions of Ito stochastic differential equations (SDEs). Recently, strong first order methods for non-commutative Ito SDEs have been proposed by the present authors. It is known that when the number of stages is large, the methods have very large stability domains in mean square (MS) for a scalar linear test equation. On the other hand, Buckwar and Sickenberger (2012) have recently proposed MS stability analyses for systems of Ito SDEs. Our aim is to investigate MS stability properties of these methods and other existing numerical schemes by their approach.