Efficient weak second-order stochastic Runge–Kutta methods for Itô stochastic differential equations

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In this paper, new weak second-order stochastic Runge–Kutta (SRK) methods for Ito stochastic differential equations (SDEs) with an m-dimensional Wiener process are introduced. Two new explicit SRK methods with weak order 2.0 are proposed. As the main innovation, the new explicit SRK methods have two advantages. First, only three evaluations of each diffusion coefficient are needed in per step. Second, the number of necessary random variables which have to be simulated is only \(m+2\) for each step. Compared to well-known explicit SRK methods, these good properties can be used to reduce the computational effort. Our methods are compared with other well-known explicit weak second-order SRK methods in numerical experiments. And the numerical results show that the computational efficiency of our methods is better than other methods.