Special versions of the collocation method for a class of integral equations of the third kind
type: Item
instance of: scholarly article
title: Special versions of the collocation method for a class of integral equations of the third kind
zbMATH Open document ID: 1258.45003
DOI: 10.3103/S1066369X12080038
author: S. A. Solov'eva
author: N. S. Gabbasov
published in: Russian Mathematics
publication date: 2012-11-20T00:00:00Z
review text: The authors consider the integral equation of the third kind \[ (Ax)(t)=(Ux)(t)+(Kx)(t)=y(t) \] where \[ (Ux)(t)=x(t)t^{p_1}(1-t)^{p_2}\prod_{j=1}^q (t-t_j)^{m_j} \] and \[ (Kx)(t)=\int_0^1K(t,s)x(s)ds,~ t\in [0,1] \] where \(p_1, p_2\in \mathbb{R}^+\), \(t_j\in(0,1)\), \(m_j\in N(j=1,\dots,q)\), \(K\) and \(y\) are known continuous functions, \(x\) is the unknown solution. They develop special direct methods for an approximate solution in the space of distributions. Some important properties of the studied methods are given.
reviewed by: Josef Kofroň
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45A05
Mathematics Subject Classification ID: 45L05
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 6108836
zbMATH Keywords: collocation method
zbMATH Keywords: third-kind integral equation
zbMATH Keywords: space of distributions
zbMATH Keywords: approximate solution
zbMATH Keywords: theoretical substantiation
MaRDI profile type: Publication
cites work: Linear Integral Equations of the Third Kind
cites work: Q5546685
cites work: Q3888485
full work available at URL: s1066369x12080038
OpenAlex ID: W2039455208
description: scientific article; zbMATH DE number 6108836