A simple Taylor-series expansion method for a class of second kind integral equations
type: Item
instance of: scholarly article
title: A simple Taylor-series expansion method for a class of second kind integral equations
zbMATH Open document ID: 0936.65146
DOI: 10.1016/S0377-0427(99)00192-2
author: Bo Zhang
author: H. Qiao
author: Yu He Ren
published in: Journal of Computational and Applied Mathematics
publication date: 2000-05-25T00:00:00Z
review text: The authors consider the integral equation \[ x(s)- \lambda \int^1_0 k(s,t)x(t) dt= y(s),\quad s\in [0,1], \] with kernel \(k\) either a continuous and (rapidly) decreasing convolution kernel, or containing a weak (algebraic) singularity. Motivated by certain limitations of the Taylor series expansion method proposed in \textit{M. Perlmutter} and \textit{R. Siegel} [ASME J. Heat Transfer, 85, 55-62 (1963)], they show how the desired Taylor coefficient functions can be found by solving a linear algebraic system which does not involve the use of boundary conditions. There is no convergence analysis, and no error estimates are given. Instead, the method is applied to three examples of integral equations with smooth kernels (arising in radiative heat transfer and electrostatics), and a constructed example with weakly singular kernel (where, not surprisingly, the method does not do well near the endpoints of the interval of integration).
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 1367865
zbMATH Keywords: second-kind integral equations
zbMATH Keywords: Fredholm integral equation
zbMATH Keywords: convolution kernel
zbMATH Keywords: Taylor series expansion method
zbMATH Keywords: radiative heat transfer
zbMATH Keywords: electrostatics
zbMATH Keywords: weakly singular kernel
reviewed by: H. Brunner
MaRDI profile type: Publication
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Wikidata QID: Q127352382
full work available at URL: s0377-0427(99)00192-2
OpenAlex ID: W2074686860
description: scientific article; zbMATH DE number 1367865