N coupled non-local harmonic oscillators leading to 2N-th order initial value problem
Numerical Analysis
2013-02-12 v1 Statistical Mechanics
Abstract
We consider a set of interwoven harmonic oscillators where the acceleration of a given oscillator is determined by the position of its nearest neighbor. We show that this problem of N non-local oscillators with periodic boundary conditions leads to a 2N-th order initial value problem. We discuss the numerical solution of this using a non-polynomial spline method. A very precise numerical method that minimizes the error can be developed, which we test for a few examples of driving forces.
Cite
@article{arxiv.1302.2482,
title = {N coupled non-local harmonic oscillators leading to 2N-th order initial value problem},
author = {Ghazala Akram and Christian Beck},
journal= {arXiv preprint arXiv:1302.2482},
year = {2013}
}
Comments
15 pages, no figures