A systematic formula for the asymptotic expansion of singular integrals
type: Item
instance of: scholarly article
title: A systematic formula for the asymptotic expansion of singular integrals
zbMATH Open document ID: 0626.45018
DOI: 10.1007/BF00948292
author: Jean-Luc Guermond
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1987-01-01T00:00:00Z
review text: The author presents a new method to obtain the asymptotic expansion of an integral with homogeneous kernel defined in terms of its finite part (FP) by considering the integral \(FP\int_{D}f(x)K(x,\epsilon)dx.\) The usefulness of the formula is depicted by two specific examples. In the first example the weight function has an explicit expression, and the other example illustrates the method with respect to a problem of applied nature in which the weight function is unknown.
Mathematics Subject Classification ID: 45L05
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 30E15
zbMATH DE Number: 4017598
zbMATH Keywords: matrix inversion
zbMATH Keywords: homogeneous kernel
zbMATH Keywords: finite part integral
zbMATH Keywords: asymptotic expansion
reviewed by: Ravinder Krishna Raina
MaRDI profile type: Publication
cites work: Q4092387
cites work: Q5816908
cites work: An alternative treatment of lifting-line theory as a perturbation problem
cites work: Singular-Perturbation Problems in Ship Hydrodynamics
cites work: Q4096019
full work available at URL: https://doi.org/10.1007/bf00948292
OpenAlex ID: W1977415182
description: scientific article; zbMATH DE number 4017598