On Algorithms for Brownian Dynamics Computer Simulations

Several Brownian Dynamics numerical schemes for treating stochastic differential equations at the position Langevin level are analyzed from the point of view of their algorithmic efficiency. The algorithms are tested using model colloidal fluid of particles interacting via the Yukawa potential. Limitations in the conventional Brownian Dynamics algorithm are shown and it is demonstrated that much better accuracy for dynamical and static quantities can be achieved with an algorithm based on the stochastic expansion and second-order stochastic Runge-Kutta algorithms. Mutual merits of the second-order algorithms are discussed.