On the numerical integration of a class of singular perturbation problems
type: Item
instance of: scholarly article
title: On the numerical integration of a class of singular perturbation problems
zbMATH Open document ID: 0633.65075
DOI: 10.1007/BF00940347
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: A three-point difference scheme recently proposed by \textit{M. K. Kadalbajoo} and \textit{Y. N. Reddy} [ibid. 51, 441-452 (1986; Zbl 0579.65081)] for the numerical solution of a class of linear, singularly perturbed, two-point boundary-value problems is investigated. The scheme is derived from a first-order approximation to the original problem with a small deviating argument. It is shown here that, in the limit, as the deviating argument tends to zero, the difference scheme converges to one- sided approximation to the original singularly perturbed equation in conservation form. The limiting scheme is shown to be stable on any uniform grid. Therefore, no advantage arises from using the deviating argument, and the most accurate and efficient results are obtained with the deviation at its zero limit.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 4030872
zbMATH Keywords: numerical stability
zbMATH Keywords: three-point difference scheme
zbMATH Keywords: singularly perturbed equation
zbMATH Keywords: conservation form
author: N. K. Nichols
MaRDI profile type: Publication
cites work: Numerical integration of a class of singular perturbation problems
cites work: Nonlinear Singular Perturbation Problems and One Sided Difference Schemes
cites work: Monotone Difference Schemes for Singular Perturbation Problems
cites work: Alternating Direction Implicit Methods
cites work: Q5559978
cites work: Q5180217
cites work: Numerical Methods for Stiff Two-Point Boundary Value Problems
description: scientific article; zbMATH DE number 4030872