A splitting-step algorithm for reflected stochastic differential equations in R+1

A new algorithm, which is based on the splitting-step idea and the penalization method, for reflected stochastic differential equation (RSDE) in the upper half-space R+1 is presented in this paper. After some important estimates about RSDEs and penalization ODEs are obtained, the local pathwise error of the suggested algorithm are considered, and an estimate of local error in the 2p2pth moment is proved under the assumptions of Lipschitz continuity and linear growth. Some numerical experiments based on MATLAB programs are given to support the suggested algorithm.