Strong Runge–Kutta Methods With order one for Numerical Solution of Itô Stochastic Differential Equations

In this paper, order conditions for coefficients of a class of stochastic Runge–Kutta (SRK) methods with strong global order 1, which applied for solving Ito stochastic differential equations (SDEs) with a single noise process, are presented. In particular, explicit twostage and three-stage SRK methods of this class with minimum principal error constants are constructed. Numerical results with two test problems of our methods, the Ito method and Milstein method will be compared.