Numerical solutions of integral equations on the half line. II: The Wiener-Hopf case
type: Item
instance of: scholarly article
title: Numerical solutions of integral equations on the half line. II: The Wiener-Hopf case
zbMATH Open document ID: 0662.65124
DOI: 10.1216/JIE-1988-1-2-203
author: Philip M. Anselone
author: Ian H. Sloan
published in: Journal of Integral Equations and Applications
publication date: 1988-01-01T00:00:00Z
review text: Numerical approximation schemes of quadrature type are investigated for integral equations of the form \[ x(s)-\int^{\infty}_{0}\kappa (s- t)x(t)dt=y(s),\quad 0\leq s<\infty. \] The principal hypotheses are that \(\kappa\) is integrable, bounded, and uniformly continuous on R, and that x and y are bounded and continuous or, alternatively, bounded and uniformly continuous, on \(R^+\). The convergence of numerical integration approximations is established, along with error bounds in some cases. The analysis involves the collectively compact operator approximation theory and a variant of that theory in which the role of compact sets is played by bounded uniformly equicontinuous sets of functions on \(R^+.\) [For part I see Numer. Math. 51, 599-614 (1987; Zbl 0613.65137).]
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 4082927
zbMATH Keywords: Banach space
zbMATH Keywords: Wiener-Hopf integral equations
zbMATH Keywords: quadrature method
zbMATH Keywords: compact integral operator
zbMATH Keywords: convergence
zbMATH Keywords: error bounds
zbMATH Keywords: collectively compact operator approximation theory
MaRDI profile type: Publication
full work available at URL: jie-1988-1-2-203
OpenAlex ID: W1964615554
description: scientific article; zbMATH DE number 4082927