A collocation method for the numerical      Fourier analysis of quasi-periodic functions.      II: Analytical error estimates

Gerard Gómez; Josep–Maria Mondelo; Carles Simó

doi:10.3934/dcdsb.2010.14.75

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2010, Volume 14, Issue 1: 75-109. Doi: 10.3934/dcdsb.2010.14.75

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A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates

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: May 31, 2009

Revised: December 31, 2009

Published: June 2010

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Abstract

In a previous paper [6], a numerical procedure for the Fourier analysis of quasi-periodic functions was developed, allowing for an accurate determination of frequencies and amplitudes from equally-spaced samples of the input function on a finite time interval. This paper is devoted to a complete error analysis of that procedure, from which computable bounds are deduced. These bounds are verified and further discussed in examples.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates

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