Numerical evaluation of hypersingular integrals
type: Item
instance of: scholarly article
title: Numerical evaluation of hypersingular integrals
zbMATH Open document ID: 0818.65016
DOI: 10.1016/0377-0427(94)90287-9
author: G. Monegato
published in: Journal of Computational and Applied Mathematics
publication date: 1994-09-22T00:00:00Z
review text: The paper is motivated by the occurrence of singular and hypersingular integrals in applied mathematics, for example Cauchy principal value and Hadamard finite-part integrals in boundary integral equations. Attention is concentrated on the less familiar two-dimensional Cauchy principal value integrals and one- and two-dimensional integrals with stronger singularities requiring interpretation as finite-part integrals. Basic definitions and properties are discussed. Methods for the numerical evaluation of these integrals are critically reviewed and a number of new results on convergence, expressions for weights, asymptotic error estimates and conditioning of rules (stability factors) are obtained. Numerical examples are included.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 41A80
zbMATH DE Number: 643741
zbMATH Keywords: singular integrals
zbMATH Keywords: quadrature
zbMATH Keywords: cubature
zbMATH Keywords: stability
zbMATH Keywords: numerical examples
zbMATH Keywords: hypersingular integrals
zbMATH Keywords: Cauchy principal value
zbMATH Keywords: Hadamard finite-part integrals
zbMATH Keywords: boundary integral equations
zbMATH Keywords: convergence
zbMATH Keywords: asymptotic error estimates
zbMATH Keywords: conditioning
reviewed by: William E. Smith
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90287-9
OpenAlex ID: W2007946663
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