Algorithms for Brownian dynamics simulation

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Abstract
Several Brownian dynamics numerical schemes for treating one-variable stochastic differential equations at the position of the Langevin level are analyzed from the point of view of their algorithmic efficiency. The algorithms are tested using a one-dimensional biharmonic Langevin oscillator process. Limitations in the conventional Brownian dynamics algorithm are shown and it is demonstrated that much better accuracy for dynamical quantities can be achieved with an algorithm based on the stochastic expansion (SE), which is superior to the stochastic second-order Runge-Kutta algorithm. For static properties the relative accuracies of the SE and Runge-Kutta algorithms depend on the property calculated.