Algorithms for Brownian dynamics computer simulations: Multivariable case

Several Brownian numerical schemes for treating stochastic differential equ ations at the position Langevin level are analyzed from the point of view o f their algorithmic efficiency for large-N systems. The algorithms are test ed using model colloidal fluids of particles interacting via the Yukawa pot ential. Limitations in the conventional Brownian dynamics algorithm are sho wn and it is demonstrated that much better accuracy for dynamical and stati c quantities can be achieved with an algorithm based on the stochastic expa nsion and second-order stochastic Runge-Kutta algorithms. The importance of the various terms in the stochastic expansion is analyzed, and the relativ e merits of second-order algorithms are discussed. [S1063-651X(99)03108-6].