Algorithms for Brownian dynamics computer simulations: Multivariable case

Several Brownian numerical schemes for treating stochastic differential equations at the position Langevin level are analyzed from the point of view of their algorithmic efficiency for large-N systems. The algorithms are tested using model colloidal fluids 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. The importance of the various terms in the stochastic expansion is analyzed, and the relative merits of second-order algorithms are discussed.