Ac. Branka et Dm. Heyes, ALGORITHMS FOR BROWNIAN DYNAMICS SIMULATION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(2), 1998, pp. 2611-2615
Several Brownian dynamics numerical schemes for treating one-variable
stochastic differential equations at the position of the Langevin leve
l 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 f
or 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 accur
acies of the SE and Runge-Kutta algorithms depend on the property calc
ulated.