A numerical method for the approximation of singular integrals of functions with a pole of order two
type: Item
instance of: scholarly article
title: A numerical method for the approximation of singular integrals of functions with a pole of order two
zbMATH Open document ID: 0811.65019
DOI: 10.1016/0168-9274(94)00040-9
author: Ioan Jadic
published in: Applied Numerical Mathematics
publication date: 1995-05-02T00:00:00Z
review text: The purpose of this paper is the derivation of approximate integration formulas for the integral \(I(\xi)= \int^ b_ a (f(x)/(x- \xi)^ 2)dx\), if the function \(f(x)\) is such that its fourth derivative \(f^{(IV)}(x)\) is continuous throughout the interval \((a,b)\). The main feature of the given method is that polynomial interpolation is carried out for the non-singular numerator rather than for the whole integrand function. The remainder terms of the presented numerical quadrature formulas are given.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A80
zbMATH DE Number: 699085
zbMATH Keywords: singular integrals
zbMATH Keywords: pole of order two
zbMATH Keywords: polynomial interpolation
zbMATH Keywords: remainder terms
zbMATH Keywords: numerical quadrature formulas
reviewed by: Dumitru Acu
MaRDI profile type: Publication
full work available at URL: 0168-9274(94)00040-9
OpenAlex ID: W2048318185
cites work: Q4772602
cites work: Lifting line theory for supersonic flow applications
cites work: Q5332459
Wikidata QID: Q127628886
description: scientific article; zbMATH DE number 699085