Uniform convergence for the difference scheme in the conservation form of ordinary differential equation with a small parameter
type: Item
instance of: scholarly article
title: Uniform convergence for the difference scheme in the conservation form of ordinary differential equation with a small parameter
zbMATH Open document ID: 0623.65088
DOI: 10.1007/BF01897208
author: Pengcheng Ling
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1986-01-01T00:00:00Z
review text: For the singular perturbation problem of the selfadjoint ordinary differential equation \[ (1)\quad Lu(x)=-\epsilon (p(x)u'(x))'+q(x)u(x)=f(x)\quad (x\in 0,1)),\quad u(0)=A,\quad u(1)=B \] with \(p(x)\geq \alpha >0\), \(q(x)\geq \beta >0\) (x\(\in [0,1])\) and \(\epsilon >0\) being a small parameter a class of difference schemes in conservation form with exponentially fitted factors \(\sigma_ i(h/\sqrt{\epsilon})\) is constructed. Sufficient conditions for \(\sigma_ i\) are derived to satisfy the purpose that the corresponding scheme is uniformly convergent to the solution of (1). In the case at issue the order of convergence is one, and under some assumption on p(x) and q(x), it is two.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 4011829
zbMATH Keywords: uniform convergence
zbMATH Keywords: singular perturbation problem
zbMATH Keywords: small parameter
zbMATH Keywords: difference schemes in conservation form
zbMATH Keywords: exponentially fitted factors
Wikidata QID: Q115393070
reviewed by: L. M. Berkovich
MaRDI profile type: Publication
cites work: Q3909948
full work available at URL: https://doi.org/10.1007/bf01897208
OpenAlex ID: W2020065352
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description: scientific article; zbMATH DE number 4011829