Asymptotic error expansion of a c error expansion of a colloation-type method for Hammerstein equations
type: Item
instance of: scholarly article
title: Asymptotic error expansion of a c error expansion of a colloation-type method for Hammerstein equations
zbMATH Open document ID: 0834.65138
DOI: 10.1016/0096-3003(94)00160-6
author: Guoqiang Han
author: L.-Q. Zhang
published in: Applied Mathematics and Computation
publication date: 1996-04-18T00:00:00Z
review text: The authors obtain an asymptotic error expansion of a collocation-type method for Hammerstein equations of the form \[ y(x) = f(x) + \int^b_a K(x,t) g(t,y(t))dt, \quad a \leq x \leq b, \] [see also \textit{S. Kumar} and \textit{I. H. Sloan}, Math. Comput. 48, 585-593 (1987; Zbl 0616.65142)]. They demonstrate that the approximate solution to \(y(x)\) admits an error expansion in even powers of the step-size \(h\), beginning with a term \(h^{2p}\), using piecewise polynomials of \(\Pi_{p-1}\). Thus Richardson's extrapolation can be performed on the solution and the accuracy of the numerical solution is greatly increased.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 803671
zbMATH Keywords: asymptotic error expansion
zbMATH Keywords: collocation
zbMATH Keywords: Hammerstein equations
zbMATH Keywords: Richardson's extrapolation
MaRDI profile type: Publication
full work available at URL: 0096-3003(94)00160-6
OpenAlex ID: W1990986596
cites work: A New Collocation-Type Method for Hammerstein Integral Equations
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description: scientific article; zbMATH DE number 803671