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

A stable and accurate algorithm for simulating massive damped Brownian motion is proposed and discussed. The algorithm, being fully integral for the friction and noise terms and predictor-corrector for the potential force in the Langevin equations, is stable upon changing time step and for various masses of the particle. In particular, the limit of zero inertia can be safely taken, and the algorithm yields naturally the corresponding overdamped case. The steady velocity of a particle moving in a titled periodic potential is calculated and three algorithms are compared.