Semi-integral scheme for simulation of Langevin equation with weak inertia

A stable and accurate algorithm for simulating massive damped Brownian moti on is proposed and discussed. The algorithm, being fully integral for the f riction and noise terms and predictor-corrector for the potential force in the Langevin equations, is stable upon changing time step and for various m asses of the particle. In particular, the limit of zero inertia can be safe ly taken, and the algorithm yields naturally the corresponding overdamped c ase. The steady velocity of a particle moving in a titled periodic potentia l is calculated and three algorithms are compared.