Numerical solution of quasilinear attractive turning point problems
type: Item
instance of: scholarly article
title: Numerical solution of quasilinear attractive turning point problems
zbMATH Open document ID: 0773.65063
DOI: 10.1016/0898-1221(92)90093-W
author: Ping Lin
author: Relja Vulanović
publication date: 1993-04-01T00:00:00Z
review text: A quasilinear Dirichlet problem with a small parameter \(-\varepsilon u''- xb(x,u)u'+c(x,u)=0\), \(x\in[-1,1]\) is considered. In order to construct a numerical method uniformly convergent in \(\varepsilon\), certain properties of the solution are investigated. The boundedness of the unique solution \(u_ \varepsilon\) is proved and the distance of the solution and its derivatives from the solution of the corresponding reduced problem \((\varepsilon=0)\) is estimated. The authors propose a difference scheme generated by non-uniform mesh points determined by a function dependent on \(\varepsilon\). The uniqueness of the discrete solution and the convergence in the discrete \(L_ 1\)-norm uniform with respect to \(\varepsilon\) is established. Numerical results testing the method are included. The paper is an extension of the result obtained previously for the semilinear case by the first author [RAIRO, Modélisation Math. Anal. Numér. 24, No. 6, 765-783 (1990; Zbl 0716.65075)].
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 148264
zbMATH Keywords: singular perturbation
zbMATH Keywords: quasilinear
zbMATH Keywords: attractive turning point
zbMATH Keywords: numerical results
zbMATH Keywords: quasilinear Dirichlet problem
zbMATH Keywords: small parameter
zbMATH Keywords: difference scheme
zbMATH Keywords: convergence
reviewed by: Teresa Regińska
MaRDI profile type: Publication
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cites work: On the Behavior of Solutions of a Singularly Perturbed Boundary Value Problem with a Turning Point
cites work: Finite-difference schemes for quasilinear singular perturbation problems
full work available at URL: 0898-1221(92)90093-w
OpenAlex ID: W2065295866
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 148264