A second-order algorithm for the simulation of the Brownian dynamics of macromolecular models

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Abstract
Most recent works on Brownian dynamics simulation employ a first-order algorithm developed by Ermak and McCammon [J. Chem. Phys. 69, 1352 (1978)]. In this work we propose the use of a second-order algorithm in which the step is a combination of two first-order steps, like in the second-order Runge–Kutta method for differential equations. Although the computer time per step is roughly doubled, the second-order algorithm is more efficient than the previous one because a given accuracy in the results can be achieved with less than half the number of steps. The new algorithm also allows for longer time steps without divergence. The advantage of the new procedure is illustrated in the simulation of four macromolecular systems: A quasirigid dumbbell, a semiflexible trumbbell, a semiflexible hinged rod, and a Gaussian polymer chain.