Numerical Method in Classical Dynamics

TL;DR

This paper introduces a set of algorithms for efficiently computing the time evolution of classical dynamical systems, starting from reversible approximations and extending to higher accuracy in multiple dimensions and particles.

Contribution

It presents a novel numerical method that improves accuracy and efficiency for simulating classical dynamics, scalable to complex multi-particle systems.

Findings

Effective algorithms for classical system evolution

Extension from single particle to many particles

Bootstrap approach for higher order accuracy

Abstract

A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show how to bootstrap easily to higher order accuracy.The method, first shown for a single particle in one dimension, is then neatly extended to many dimensions and many particles.