A Gear-like Predictor-Corrector method for Brownian Dynamics Simulation

We introduce a Predictor-Corrector type method suitable for performing many-particle Brownian Dynamics simulations. Since the method goes over to the Gear's method for Molecular Dynamics simulation in the limit of vanishing friction, we refer to it as a Gear-like algorithm. The algorithm has been tested on a one-dimensional, stochastically damped harmonic oscillator model, showing that it can cover a wide range of friction coefficients with a high-order accuracy, excellent stability, and a very small energy drift on the long time scales.