A patch that imparts unconditional stability to explicit integrators for Langevin-like equations

Authors:
Nawaf Bou-Rabee;Eric Vanden-Eijnden
Affiliations:
Department of Mathematical Sciences, Rutgers University, 311 N 5th Street, Camden, NJ 08102, USA;Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, USA
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

This paper extends the results in [8] to stochastic differential equations (SDEs) arising in molecular dynamics. It implements a patch to explicit integrators that consists of a Metropolis-Hastings step. The 'patched integrator' preserves the SDE's equilibrium distribution and is accurate on finite time intervals. As a corollary this paper proves the integrator's accuracy in estimating finite-time dynamics along an infinitely long solution - a first in molecular dynamics. The paper also covers multiple time-steps, holonomic constraints and scalability. Finally, the paper provides numerical tests supporting the theory.