Modifying the split-step theta-method with harmonic-mean term for stochastic differential equations

[EN] In this paper, we design a class of general split-step methods for solving Ito stochastic differential systems, in which the drift or deterministic increment function can be taken from special ordinary differential equations solver, based on the harmonic-mean. This method is justified to have a strong convergence order of 1/2. Further, we investigate mean-square stability of the proposed method for linear scalar stochastic differential equation. Finally, some examples are included to demonstrate the validity and efficiency of the introduced scheme.