Abstract
In this paper, a new pathwise approximation method is constructed to obtain approximate solutions of order 5/2 for Ito stochastic differential 2 equations (SDEs). The new method does not require the simulation of the iterated stochastic integrals I-alpha, they are replaced by random variables with the same moments conditional on the linear term. The construction of the scheme is based on stochastic Ito-Taylor expansion and employing the Runge-Kutta method. It has been assumed a non-degenerated and global Lipschitz condition for the diffusion matrix b(ik). Numerical example is provided to support the validity of this new method.