Abstract: A quasi-local vibration algorithm is proposed to simulate the damped stochastic differential equations.Using the potential Taylor expansion and the operator splitting technique,the time evolution operator of a dissipative particle is factorized into two parts: an operator which describes the deterministic path of the system and a diffusion operator which incorporates fluctuation away from path.The differential equation corresponding to the fluctuation process is solved analytically, and the deterministic trajectory equation is calculated with the Euler algorithm.Compared with other algorithms, it is shown that the calculated results by the present algorithm are more stable and converge to the correct value when the time step is large.

Key words: operator splitting, Langevin equation, quasi-local vibration, stableness