Numerical integration of a class of singular perturbation problems
type: Item
instance of: scholarly article
title: Numerical integration of a class of singular perturbation problems
zbMATH Open document ID: 0579.65081
DOI: 10.1007/BF00940284
author: M. K. Kadalbajoo
author: Y. N. Reddy
published in: Journal of Optimization Theory and Applications
publication date: 1986-01-01T00:00:00Z
review text: We discuss an approximate method for the numerical integration of a class of linear, singularly perturbed two-point boundary-value problems in ordinary differential equations with a boundary layer on the left end of the underlying interval. This method requires a minimum of problem preparation and can be implemented easily on a computer. We replace the original singular perturbation problem by an approximate first-order differential equation with a small deviating argument. Then, we use the trapezoidal formula to obtain the three-term recurrence relationship. Discrete invariant imbedding algorithm is used to solve a tridiagonal algebraic system. The stability of this algorithm is investigated. The proposed method is iterative on the deviating argument. Several numerical experiments are included to demonstrate the efficiency of the method.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 3928250
zbMATH Keywords: boundary layer
zbMATH Keywords: trapezoidal formula
zbMATH Keywords: discrete invariant imbedding algorithm
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00940284
OpenAlex ID: W2080357803
description: scientific article; zbMATH DE number 3928250