Indefinite integration of oscillatory functions by the Chebyshev series expansion
type: Item
instance of: scholarly article
title: Indefinite integration of oscillatory functions by the Chebyshev series expansion
zbMATH Open document ID: 0613.65145
DOI: 10.1016/0377-0427(87)90035-5
author: Takemitsu Hasegawa
author: Tatsuo Torii
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The integral \(I(\omega,x)=\int^{x}_{0}f(t)e^{i\omega t}dt\), \(0\leq x\leq 1\), is considered. There exists much literature for the case \(x=1\) for the case \(\omega =0\). For I(\(\omega\),x) the function f(t) is approximated by a finite sum of shifted Chebyshev polynomials of the first kind. An error estimate of the approximated integral is given. The method obtained, combined with the extrapolation method due to \textit{A. Sidi} [J. Inst. Math. Appl. 26, 1-20 (1980; Zbl 0464.65002), Math. Comput. 38, 517-529 (1982; Zbl 0508.65011)] provides a quadrature scheme for the integrals \(\int^{\infty}_{a}f(x)\cos \omega x dx\), \(\int^{\infty}_{a}f(x)\sin \omega x dx\).
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 42A15
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 3992904
zbMATH Keywords: indefinite integration of oscillatory function
zbMATH Keywords: automatic quadrature
zbMATH Keywords: Chebyshev series expansion
zbMATH Keywords: three term recurrence
zbMATH Keywords: oscillatory infinite integral
zbMATH Keywords: Sidi's extrapolation
reviewed by: Antonio de Castro
describes a project that uses: QUADPACK
MaRDI profile type: Publication
full work available at URL: 0377-0427(87)90035-5
OpenAlex ID: W2085712018
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description: scientific article; zbMATH DE number 3992904