Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability
type: Item
instance of: scholarly article
title: Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability
zbMATH Open document ID: 0634.41018
DOI: 10.1016/0377-0427(87)90041-0
author: Avram Sidi
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: In a previous paper (Math. Comp. 38, 517-529 (1982; Zbl 0508.65011) the author develops an extrapolation procedure named W-transformation for numerically evaluating the infinite integrals \(\int^{\infty}_{a}f(t)dt\), \(a\geq 0\), where f is integrable at infinity. The author considers the problem of numerically evaluating the divergent integrals \(\int^{\infty}_{a}f(t)dt\), \(a\geq 0\), where f is not integrable at infinity. These integrals are defined in the sense of Abel summability. The author shows that the W-transformation can be used in evaluating these integrals efficiently.
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 4032288
zbMATH Keywords: extrapolation procedure
zbMATH Keywords: W-transformation
zbMATH Keywords: Abel summability
MaRDI profile type: Publication
full work available at URL: 0377-0427(87)90041-0
OpenAlex ID: W1963650052
cites work: The evaluation of oscillatory integrals with infinite limits
cites work: Spectral localization of operators in Banach spaces
cites work: Comparison of some methods for evaluating infinite range oscillatory integrals
cites work: Development of non-linear transformations for improving convergence of sequences
cites work: Q3228715
cites work: Extrapolation Methods for Oscillatory Infinite Integrals
cites work: The Numerical Evaluation of Very Oscillatory Infinite Integrals by Extrapolation
cites work: An algorithm for a special case of a generalization of the Richardson extrapolation process
cites work: On a Device for Computing the e m (S n ) Transformation
description: scientific article; zbMATH DE number 4032288