Inertial stochastic dynamics. I. Long-time-step methods for Langevin dynamics

Two algorithms are presented for integrating the Langevin dynamics equation with long numerical time steps while treating the mass terms as finite. The development of these methods is motivated by the need for accurate methods for simulating slow processes in polymer systems such as two-site intermolecular distances in supercoiled DNA, which evolve over the time scale of milliseconds. Our new approaches refine the common Brownian dynamics (BD) scheme, which approximates the Langevin equation in the highly damped diffusive limit. Our LTID (“long-time-step inertial dynamics”) method is based on an eigenmode decomposition of the friction tensor. The less costly integrator IBD (“inertial Brownian dynamics”) modifies the usual BD algorithm by the addition of a mass-dependent correction term. To validate the methods, we evaluate the accuracy of LTID and IBD and compare their behavior to that of BD for the simple example of a harmonic oscillator. We find that the LTID method produces the expected correlation str...