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2010, Volume 14, Issue 1: 41-74. Doi: 10.3934/dcdsb.2010.14.41
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A collocation method for the numerical Fourier analysis of quasi-periodic functions. I: Numerical tests and examples

  • 1.

    Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona

  • 2.

    Departament de Matemátiques, Universitat Autónoma de Barcelona, Edifici C, 08193 Bellaterra (Barcelona)

Received:  August 31, 2009
Revised:  December 31, 2009
Published:  June 2010
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    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].
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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