Web of Science: 10 citations, Scopus: 11 citations, Google Scholar: citations
A theoretical basis for the Harmonic Balance method
García Saldaña, Johanna Denise (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date: 2013
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.
Note: Número d'acord de subvenció MICINN/MTM2008-03437
Note: Número d'acord de subvenció AGAUR/2009/SGR-410
Rights: Tots els drets reservats.
Language: Anglès.
Document: article ; recerca ; submittedVersion
Subject: Balance harmonic method ; Planar polynomial system ; Hyperbolic limit cycle ; Fourier series ; Fixed point theorem
Published in: Journal of Differential Equations, Vol. 254 Núm. 1 (2013) , p. 67-80, ISSN 0022-0396

DOI: 10.1016/j.jde.2012.09.011


Preprint
17 p, 381.0 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2016-05-06, last modified 2019-02-28



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