Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods
type: Item
instance of: scholarly article
title: Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods
zbMATH Open document ID: 0969.65076
DOI: 10.1155/S0161171200000910
author: Dialla Konate
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2001-09-25T00:00:00Z
full work available at URL: https://eudml.org/doc/48908
review text: The author considers initial value problems for singularly perturbed equations of arbitrary order \(m\) of the form: \( \varepsilon u^{(m)} + \sum_{i=0}^{m-1} a_i u^{(i)} = f \) with \( x \in (a,b) \), stating that they are known as diffusion-convection problems. However in the standard literature these kind of problems are usually described by boundary value problems for second order equations and there is a large number of publications on their numerical solution on non uniform grids. Concerning the aim of the paper the author states: ``We start from a precise localization of the boundary layer then we decompose the domain of study, say \( \Omega \) into the boundary layer, say \( \Omega_{\varepsilon} \) and its complementary \(\Omega_0\). Next we go to the heart of our work which is to make a repeated use of the collocation method. We show that the second generation of polynomial approximation is convergent and it yields an improved error bound compared with those usually appearing in the literature''.
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 1533310
zbMATH Keywords: singularly perturbation
zbMATH Keywords: initial value problems
zbMATH Keywords: collocation methods
zbMATH Keywords: boundary layer
zbMATH Keywords: error bound
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1533310