Collocation with Chebyshev polynomials for a hypersingular integral equation on an interval
type: Item
instance of: scholarly article
title: Collocation with Chebyshev polynomials for a hypersingular integral equation on an interval
zbMATH Open document ID: 0762.65093
DOI: 10.1016/0377-0427(92)90267-2
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-18T00:00:00Z
review text: The hypersingular integral operator \(D\) defined by \(Dv(x)=- (1/\pi)\text{p.f.} \int_{-1}^ 1 v(y)(x-y)^{-2}dy\), \(x\in[-1,1]\), has the property \(D(\omega U_ j)=(j+1)U_ j\), \(j=0,1,2,\dots,\) where \(\omega(x)=(1-x^ 2)^{1/2}\) and \(U_ j\) is the Chebyshev polynomial of the second kind. The authors use this property to design and analyse the convergence rate of a collocation method for the equation \(Dv=g\) with a given smooth function \(g\).
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 85931
zbMATH Keywords: hypersingular integral operator
zbMATH Keywords: convergence rate
zbMATH Keywords: collocation method
author: V. J. Ervin
author: Ernst P. Stephan
reviewed by: G. Vainikko
MaRDI profile type: Publication
full work available at URL: 0377-0427(92)90267-2
OpenAlex ID: W1977010688
cites work: The convergence of spline collocation for strongly elliptic equations on curves
cites work: On the solution of integral equations with strongly singular kernels
cites work: On the Asymptotic Convergence of Collocation Methods With Spline Functions of Even Degree
cites work: Collocation with Chebyshev polynomials for Symm's integral equation on an interval
cites work: A hypersingular boundary integral method for two-dimensional screen and crack problems
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description: scientific article; zbMATH DE number 85931