Solution of a class of Volterra integral equations with singular and weakly singular kernels
type: Item
instance of: scholarly article
title: Solution of a class of Volterra integral equations with singular and weakly singular kernels
zbMATH Open document ID: 1148.45002
author: Elsie Sterbin Gottlieb
published in: Applied Mathematics and Computation
publication date: 2008-06-11T00:00:00Z
review text: The purpose of the paper is to derive the solution to a Volterra integral equation \[ y(t)=g(t)+\int^t_0\frac{s^{\mu-\nu}}{t^\mu}y(s)\,ds\quad (0<t<T), \] where \(\mu\) and \(\nu\) are constants, and \(g(t)\) a given function. Set \[ \varphi(t)=\int^t_0{s^{\mu-\nu}}y(s)\,ds \quad (0<t<T). \] Then the Volterra integral equation is transformed into a first-order ordinary differential equation \[ t^\nu\frac{d\varphi}{dt}=t^\mu g(t)+\varphi(t)\quad (0<t<T). \] Based on such a transformation, the authors derive analytically a general solution to the Volterra integral equation.
reviewed by: Jin Liang
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 5286409
zbMATH Keywords: Volterra integral equation
zbMATH Keywords: singular kernel
zbMATH Keywords: ordinary differential equation
zbMATH Keywords: analytic solution
MaRDI profile type: Publication
full work available at URL: j.amc.2007.09.058
OpenAlex ID: W2062032624
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DOI: 10.1016/J.AMC.2007.09.058
description: scientific article; zbMATH DE number 5286409