An extrapolation method for a Volterra integral equation with weakly singular kernel
type: Item
instance of: scholarly article
title: An extrapolation method for a Volterra integral equation with weakly singular kernel
zbMATH Open document ID: 0878.65118
DOI: 10.1016/S0168-9274(97)00016-0
author: M. Teresa Diogo
author: Pedro M. Lima
published in: Applied Numerical Mathematics
publication date: 1998-01-05T00:00:00Z
review text: Subject of the study is the Volterra integral equation of the second kind \[ u(t)= \int_0^t K(t,s)p(t,s)u(s)ds+ f(t),\qquad t\in[0,T], \] \[ \text{with }p(t,s):={1\over\sqrt\pi}\frac{1}{\sqrt{[\ln(t/s)]}} \frac{s^{\mu-1}}{t^{\mu-1}} \qquad \text{or}\quad p(t,s):=\frac{s^{\mu-1}}{t^\mu}, \] where \(\mu>0\), \(K(t,s)\) smooth and \(f\) at least differentiable in the theorems. An asymptotic error expansion of Euler's method is developed to affiliate Richardson extrapolation. Some numerical examples.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 1036649
zbMATH Keywords: Volterra integral equation
zbMATH Keywords: asymptotic error expansion
zbMATH Keywords: Euler's method
zbMATH Keywords: Richardson extrapolation
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
cites work: Q4107451
cites work: Extrapolation methods theory and practice
cites work: Asymptotic Expansions for Product Integration
cites work: High order product integration methods for a Volterra integral equation with logarithmic singular kernel
cites work: A Hermite-Type Collocation Method for the Solution of an Integral Equation with a Certain Weakly Singular Kernel
cites work: Existence, uniqueness and smoothness results for second-kind Volterra equations with weakly singular kernels
cites work: An extrapolation method with step size control for nonlinear Volterra integral equations
cites work: A spectral approach to an integral equation
cites work: Numerical Quadrature and Asymptotic Expansions
cites work: Q4749146
cites work: On an integral equation of Šub-Sizonenko
cites work: Inversion of one integral operator by the method of expansion with respect to orthogonal Watson operators
cites work: Product integration methods for an integral equation with logarithmic singular kernel
full work available at URL: s0168-9274(97)00016-0
OpenAlex ID: W2056469120
description: scientific article; zbMATH DE number 1036649