Adding an energy-like conservation law to the leapfrog integrator

TL;DR

This paper introduces a modified leapfrog integrator that incorporates an additional energy-like conservation law by embedding molecular dynamics within a larger dynamical system, enhancing stability and conservation properties.

Contribution

The paper presents a novel modification to the leapfrog integrator that embeds it into a larger dynamical system to conserve an energy-like quantity.

Findings

Enhanced stability in molecular dynamics simulations

Conservation of an additional energy-like quantity

Potential for improved long-term simulation accuracy

Abstract

The leapfrog integrator is widely used because of its excellent stability in molecular dynamics simulation. This is recognized as being due to the existence of a discrete variational structure of the equations. We introduce a modified leapfrog method which includes an additional energy-like conservation law by embedding a molecular dynamics simulation within a larger dynamical system.