One class of conservative difference schemes for solving molecular dynamics equations of motion

TL;DR

This paper introduces a new class of symmetric simplectic numerical schemes for molecular dynamics that improve stability and Hamiltonian conservation over large time intervals compared to traditional methods.

Contribution

It proposes a novel approach to constructing symmetric simplectic schemes with specified accuracy, enhancing stability and conservation in molecular dynamics simulations.

Findings

Third order scheme is more stable than second order velocity Verlet.

The new scheme conserves the Hamiltonian more accurately over large intervals.

Numerical experiments confirm improved stability and accuracy.

Abstract

Simulation of many-particle system evolution by molecular dynamics takes to decrease integration step to provide numerical scheme stability on the sufficiently large time interval. It leads to a significant increase of the volume of calculations. An approach for constructing symmetric simplectic numerical schemes with given approximation accuracy in relation to integration step, for solving molecular dynamics Hamiltonian equations, is proposed in this paper. Numerical experiments show that obtained under this approach symmetric simplectic third order scheme is more stable for integration step, time-reversible and conserves Hamiltonian of the system with more accuracy at a large integration interval then second order velocity Verlet numerical schemes.