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Efficient weak second-order stochastic Runge-Kutta methods for Itô stochastic differential equations. (English) Zbl 1359.60086

Summary: In this paper, new weak second-order stochastic Runge-Kutta (SRK) methods for Itô 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.

MSC:

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
60F05 Central limit and other weak theorems
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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