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| Pàgina inicial > Articles > Articles publicats > A theoretical basis for the Harmonic Balance method |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Data: | 2013 |
| Resum: | 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. |
| Ajuts: | Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
| Drets: | Tots els drets reservats.  |
| Llengua: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Matèria: | Balance harmonic method ; Planar polynomial system ; Hyperbolic limit cycle ; Fourier series ; Fixed point theorem |
| Publicat a: | Journal of differential equations, Vol. 254 Núm. 1 (2013) , p. 67-80, ISSN 1090-2732 |
17 p, 381.0 KB |
