Fast integration of rapidly oscillatory functions
type: Item
instance of: scholarly article
title: Fast integration of rapidly oscillatory functions
zbMATH Open document ID: 0858.65017
DOI: 10.1016/0377-0427(94)00118-9
author: Yanyan Li
published in: Journal of Computational and Applied Mathematics
publication date: 1997-03-25T00:00:00Z
review text: The author considers the problem of computing integrals of rapidly oscillatory functions of the type \[ I= \int^b_a g(x)S(rx)dx, \tag{1} \] where \(S\) is an oscillatory function, \(r\) is a large parameter and \(a\) and \(b\) are real and finite. The problem of computing the integral (1) is replaced by a problem of finding a solution of a system of linear ordinary differential equations, with no boundary conditions. This last problem is solved by the collocation method. The particular case for integrals involving Bessel functions \(J_\gamma (rx)\) with large oscillation parameter \(r\) is used as an example.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 65L60
zbMATH DE Number: 908357
zbMATH Keywords: integrals of rapidly oscillatory functions
zbMATH Keywords: collocation method
zbMATH Keywords: integrals involving Bessel functions
reviewed by: Dumitru Acu
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)00118-9
OpenAlex ID: W1966478028
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description: scientific article; zbMATH DE number 908357