Asymptotic analysis of a Volterra integral equation
type: Item
instance of: scholarly article
title: Asymptotic analysis of a Volterra integral equation
zbMATH Open document ID: 0658.45014
DOI: 10.1016/0893-9659(88)90086-9
author: D. Glenn Lasseigne
published in: Applied Mathematics Letters
publication date: 1988-01-01T00:00:00Z
review text: A Volterra integral equation of the form \(u(t)=\epsilon \int^{t}_{0}[\pi (t-s)]^{-1/2}F(u(s),s)ds\) is considered where \(F(0,t)\sim c_ 0t^{-r_ 0}\) and \(F_ u(0,t)\sim -c_ 1t^{-r_ 1}\) as \(t\to +\infty\) and \(r_ 1<1/2\). Writing \(u(t)\sim \epsilon u_ 0(t)+\Delta (\epsilon)v_ 0(\tau)+...,\) where \(\tau =\epsilon^{\alpha}t,\quad \alpha =2/(1-2r_ 1)\) is the large-time variable a method is suggested to obtain \(v_ 0\).
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45M05
zbMATH DE Number: 4075792
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: Volterra integral equation
reviewed by: George Karakostas
MaRDI profile type: Publication
full work available at URL: 0893-9659(88)90086-9
OpenAlex ID: W2039662482
cites work: Singularly Perturbed Volterra Integral Equations
cites work: Asymptotic Solution to a Class of Nonlinear Volterra Integral Equations. II
cites work: Singularly Perturbed Volterra Integral Equations II
cites work: Asymptotic solution of some singularly perturbed Fredholm integral equations
description: scientific article; zbMATH DE number 4075792