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Approximation of multiple integrals by simple integrals involving periodic functions

A. Benabidallah (USTHB, Faculté de Maths, Alger, Algeria Université Paris VI, Paris, France)
Y. Cherruault (Université Paris VI, Paris, France)
G. Mora (Department of Mathematical Analysis and Applied Mathematics, Faculty of Sciences, University of Alicante, Alicante, Spain)

Kybernetes

ISSN: 0368-492X

Article publication date: 1 October 2004

Abstract

In this paper, we consider problems of numerical integration of fast oscillatory functions of one variable, obtained by using α‐dense curves and approximating multiple integrals. Using first, periodic and regular α‐dense curves we propose a trapezoidal formula for calculating the periodic integrand obtained. Then, we consider the simple integrals as integrals with weight. We propose a method to evaluate the moments of the weight function. This allows us to build a recurrent formula for the orthogonal polynomials family and to use a Gaussian rule to estimate the simple integral. Finally, we adapt the Filon's method, consisting in evaluating the Fourier coefficients of a function, to the oscillatory integrand obtained by using reducing transformations.

Keywords

Citation

Benabidallah, A., Cherruault, Y. and Mora, G. (2004), "Approximation of multiple integrals by simple integrals involving periodic functions", Kybernetes, Vol. 33 No. 9/10, pp. 1472-1490. https://doi.org/10.1108/03684920410534470

Publisher

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Emerald Group Publishing Limited

Copyright © 2004, Emerald Group Publishing Limited