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

2016/05/18 by E. G. Nikonov, Nikonov, Eduard G.
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1605.05714

openalex publication_date 2016/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Polynomial propagators for classical molecular dynamics
• A New Time-Reversible Integrator for Molecular Dynamics Applications
• Effective conservation of energy and momentum algorithm using switching potentials suitable for molecular dynamics simulation of thermodynamical systems
• Explicit Symplectic Integrators of Molecular Dynamics Algorithms for Rigid-Body Molecules in the Canonical, Isothermal-Isobaric, and Related Ensembles
• On conservative difference schemes for the many-body problem