In this paper, we describe stochastic Runge–Kutta (SRK) methods with strong order 1.0 for strong solutions of Stratonovich stochastic differential equations (SDEs) which was first introduced by Burrage and Burrage in 1996. In particular, three new SRK methods with strong order 1.0 are constructed. They are an explicit two–stage method, an explicit three–stage method with minimum principal error coefficients and an implicit three–stage method with minimum principal error coefficients. Numerical results for two test problems with our methods and Burrage’s method and Platen method will be compared.

Keywords