On the solution of a special kind of singular integral equation
type: Item
instance of: scholarly article
title: On the solution of a special kind of singular integral equation
zbMATH Open document ID: 0877.45001
author: Olaf Hansen
published in: Journal of Integral Equations and Applications
publication date: 1997-12-10T00:00:00Z
review text: While using the inversion formula for a Cauchy type singular integral equation to approximate numerically the solution, the author deals with the case where the solution is not continuously differentiable, but is in a special class of Hölder continuous functions, \(C^\alpha(L,\mathbb{C})\) on a simple, closed smooth curve in \(\mathbb{C}\) with the usual norm \(|\cdot|_{C^\alpha(L,\mathbb{C})}\). The integral equation is \[ {1\over\pi i} \int_L {\phi(t)\over t-t_0} dt= \psi(t_0),\quad t_0\in L \] and its solution is \[ \phi(t_0)= {1\over\pi i} \int_L {\psi(t)\over t-t_0} dt,\quad t_0\in L, \] where \(\phi\in C^\alpha([0,2\pi],\mathbb{C})\). Various sections of the paper give appropriate concepts, definitions and formulae, so employed.
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 1029188
zbMATH Keywords: Hölder space
zbMATH Keywords: weakly singular solution
zbMATH Keywords: Cauchy type singular integral equation
reviewed by: P. K. Banerji
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075970
OpenAlex ID: W2094345016
cites work: Midpoint collocation for Cauchy singular integral equations
cites work: An optimal order collocation method for first kind boundary integral equations on polygons
cites work: The use of piecewise quadratic polynomials for the solution of singular integral equations of Cauchy type
cites work: A method for the numerical solution of singular integral equations with a principal value integral
cites work: Q5820804
cites work: Q5683194
cites work: Q5508372
DOI: 10.1216/JIEA/1181075970
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description: scientific article; zbMATH DE number 1029188