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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

A collocation method for the numerical Fourier analysis of quasi-periodic functions. I: Numerical tests and examples

Pages: 41 - 74, Volume 14, Issue 1, July 2010      doi:10.3934/dcdsb.2010.14.41

 
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Gerard Gómez - Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain (email)
Josep–Maria Mondelo - Departament de Matemátiques, Universitat Autónoma de Barcelona, Edifici C, 08193 Bellaterra (Barcelona), Spain (email)
Carles Simó - Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain (email)

Abstract: The purpose of this paper is to develop a numerical procedure for the determination of frequencies and amplitudes of a quasi--periodic function, starting from equally-spaced samples of it on a finite time interval. It is based on a collocation method in frequency domain. Strategies for the choice of the collocation harmonics are discussed, in order to ensure good conditioning of the resulting system of equations. The accuracy and robustness of the procedure is checked with several examples. The paper is ended with two applications of its use as a dynamical indicator. The theoretical support for the method presented here is given in a companion paper [21].

Keywords:  Numerical Fourier analysis, Fast Fourier Transform, collocation method, quasi-periodic functions.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: September 2009;      Revised: January 2010;      Available Online: April 2010.