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[Abstract = "Several Brownian Dynamics numerical schemes for treating stochastic differential equations atthe position Langevin level are analyzed from the point of view of their algorithmic efficiency. The algorithmsare tested using model colloidal fluid of particles interacting via the Yukawa potential. Limitationsin the conventional Brownian Dynamics algorithm are shown and it is demonstrated that much betteraccuracy for dynamical and static quantities can be achieved with an algorithm based on the stochasticexpansion and second-order stochastic Runge-Kutta algorithms. Mutual merits of the second-order algorithmsare discussed."]