On the convergence of the method for indefinite integration of oscillatory and singular functions
type: Item
instance of: scholarly article
title: On the convergence of the method for indefinite integration of oscillatory and singular functions
zbMATH Open document ID: 1203.65051
author: Paweł Keller
author: Paweł Woźny
published in: Applied Mathematics and Computation
publication date: 2010-05-11T00:00:00Z
review text: In 2007, the first author [Numer. Algorithms 46, No. 3, 219--251 (2007; Zbl 1131.65025)] proposed an efficient method for computing indefinite integrals of the form \[ I(y)=\int_{-1}^{y}G(x)K(x) dx\,\,\,(-1\leq y\leq 1), \tag{1} \] where \(G\) is a smooth function, while the function \(K\) is highly oscillatory and may possess singularity points. In the present paper the authors assume that \(K\) is absolutely integrable. It is considered the problem to approximate the integral (1) with a uniform error less then a given value of error tolerance. In this article are analyzed the properties of the difference operator related to the difference equation for the Chebyshev coefficients of a function that satisfies a given linear differential equation with polynomial coefficients. They are presented the results of numerical experiments verifying the reliability of the error estimations proved in this paper.
reviewed by: Ana Maria Acu
Mathematics Subject Classification ID: 65D30
zbMATH DE Number: 5707079
zbMATH Keywords: indefinite integration
zbMATH Keywords: oscillatory function
zbMATH Keywords: singular function
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: linear difference operator
zbMATH Keywords: linear difference equation
describes a project that uses: Clenshaw-Curtis
MaRDI profile type: Publication
full work available at URL: j.amc.2010.01.117
OpenAlex ID: W1992711913
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DOI: 10.1016/J.AMC.2010.01.117
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description: scientific article; zbMATH DE number 5707079