an efficient Runge-Kutta scheme for solutions of Ito stochastic differential equations

In this paper, a higher order scheme of numerical approximation is presented for stochastic differential equations of Ito type, where a stochastic version of Runge-Kutta (RK) scheme has been developed to evaluate the coefficients of Ito equations. The iterative evaluation has been performed for both drift and dispersion functions. To achieve higher order accuracy the present RK scheme is organized by 4 types of terms. The numerical solution generated by the 4-stage explicit RK scheme has 1.5 order accuracy and the asymptotic efficiency. The results of simulation experiments are shown for supporting the validity of the approximation scheme