A patch that imparts unconditional stability to certain explicit integrators for SDEs

Details A patch that imparts unconditional stability to certain explicit integrators for SDEs A patch that imparts unconditional stability to certain explicit integrators for SDEs

2010-10-20

arxiv.org/abs/1010.4278v1

Mathematics

Numerical Analysis

29 pages, 5 figures

Scientific paper

This paper proposes a simple strategy to simulate stochastic differential equations (SDE) arising in constant temperature molecular dynamics. The main idea is to patch an explicit integrator with Metropolis accept or reject steps. The resulting `Metropolized integrator' preserves the SDE's equilibrium distribution and is pathwise accurate on finite time intervals. As a corollary the integrator can be used to estimate finite-time dynamical properties along an infinitely long solution. The paper explains how to implement the patch (even in the presence of multiple-time-stepsizes and holonomic constraints), how it scales with system size, and how much overhead it requires. We test the integrator on a Lennard-Jones cluster of particles and `dumbbells' at constant temperature.

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