Algorithms for Brownian dynamics simulation

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;md 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.