Stochastic Runge-Kutta methods with deterministic high order for ordinary differential equations
We consider embedding deterministic Runge-Kutta methods with high order into weak order stochastic Runge-Kutta (SRK) methods for non-commutative stochastic differential equations (SDEs). As a result, we have obtained weak second order SRK methods which have good properties with respect to not only practical errors but also mean square stability. In our stability analysis, as well as a scalar test equation with complex-valued parameters, we have used a multi-dimensional non-commutative test SDE. The performance of our new schemes will be shown through comparisons with an efficient and optimal weak second order scheme proposed by Debrabant and Rler (Appl. Numer. Math. 59:582594, 2009).
weak second order mean square stability explicit method it stochastic differential equation 65c30 60h10 60h35