A theoretical basis for the Harmonic Balance Method
Classical Analysis and ODEs
2012-02-09 v1 Dynamical Systems
Abstract
The Harmonic Balance method provides a heuristic approach for finding truncated Fourier series as an approximation to the periodic solutions of ordinary differential equations. Another natural way for obtaining these type of approximations consists in applying numerical methods. In this paper we recover the pioneering results of Stokes and Urabe that provide a theoretical basis for proving that near these truncated series, whatever is the way they have been obtained, there are actual periodic solutions of the equation. We will restrict our attention to one-dimensional non-autonomous ordinary differential equations and we apply the results obtained to a couple of concrete examples coming from planar autonomous systems.
Cite
@article{arxiv.1202.1791,
title = {A theoretical basis for the Harmonic Balance Method},
author = {Johanna D. García-Saldaña and Armengol Gasull},
journal= {arXiv preprint arXiv:1202.1791},
year = {2012}
}