A pseudospectral method for Hammerstein equations
type: Item
instance of: scholarly article
title: A pseudospectral method for Hammerstein equations
zbMATH Open document ID: 0856.65148
author: M. Razzaghi
author: Gamal N. Elnagar
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-07-14T00:00:00Z
review text: The paper is concerned with the numerical solution of the Hammerstein integral equation \[ y(t) - \int^1_0k(t,s)g \bigl(s,y(s) \bigr)ds=f(t), \quad t\in[-1,1], \tag{1} \] with \(g\) nonlinear in \(y\). The proposed method is applied not to equation (1), but rather to an equivalent equation \(z(t) = g(t,y(t))\), where \(z\) is approximated by algebraic polynomials, with coefficients determined by collocating at the Gauss-Legendre-Lobatto nodes. The authors establish uniform convergence of the approximate solutions and present numerical examples.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 902543
zbMATH Keywords: collocation
zbMATH Keywords: pseudospectral method
zbMATH Keywords: Hammerstein integral equation
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
reviewed by: Johannes Elschner
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0162
OpenAlex ID: W1992344330
DOI: 10.1006/JMAA.1996.0162
description: scientific article; zbMATH DE number 902543