A new variant of the subdomain method for integral equations of the third kind with singularities in the kernel
type: Item
instance of: scholarly article
title: A new variant of the subdomain method for integral equations of the third kind with singularities in the kernel
zbMATH Open document ID: 1232.45007
DOI: 10.3103/S1066369X11050021
author: R. R. Zamaliev
author: N. S. Gabbasov
published in: Russian Mathematics
publication date: 2011-11-21T00:00:00Z
review text: The authors study integral equations of the third kind with fixed singularities in the kernel. The integral is understood in the sense of the Hadamard finite part. They construct a new variant of the subdomain method for the approximate solution in the space of generalized functions. They prove the unique solvability of the corresponding approximate equation, estimate the error of the approximate solution and prove the convergence of a sequence of approximate solutions to the exact one. The stability and well-posedness of the approximating equations are also studied.
reviewed by: Adrian Carabineanu
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 5975537
zbMATH Keywords: integral equations of the third kind
zbMATH Keywords: space of generalized functions
zbMATH Keywords: approximate solution
zbMATH Keywords: subdomain method
zbMATH Keywords: theoretical justification
zbMATH Keywords: error estimate
MaRDI profile type: Publication
cites work: Linear Integral Equations of the Third Kind
cites work: Q5546685
cites work: Methods for solving an integral equation of the third kind with fixed singularities in the kernel
cites work: Q3212247
cites work: Q4533293
cites work: Q3209136
full work available at URL: s1066369x11050021
OpenAlex ID: W2017536448
description: scientific article; zbMATH DE number 5975537