Numerical techniques for a class of singular perturbation problems
type: Item
instance of: scholarly article
title: Numerical techniques for a class of singular perturbation problems
zbMATH Open document ID: 0703.65042
DOI: 10.1016/0096-3003(90)90089-L
author: Y. N. Reddy
published in: Applied Mathematics and Computation
publication date: 1990-01-01T00:00:00Z
review text: An efficient two part numerical method is derived for approximate solution of a singularly perturbed second order boundary value problem for an ordinary differential equation. The system considered has the form (i) \(\epsilon y''+a(x)y'+b(x)y=f(x)\), \(0<x<1\), (ii) \(y(0)=\alpha\), \(y(1)=\beta\). The procedure used is to replace the given equation with a corresponding differential equation of first order having a small retarding argument \(\delta\). Then the new equation is approximated for various \(\delta\) at mesh points by a tridiagonal matrix system which is solved by a discrete invariant embedding technique. Solutions of the retarded system are computed for a sequence of the parameter \(\delta_ n\) until \(| y(x,\delta_{n+1})-y(x,\delta_ n)| <\sigma\) where \(\sigma\) is a given tolerance. Numerical results presented for three examples with known solutions indicate that the method leads to good approximations. Two methods are given for setting up the equation with a retarding argument.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34K10
zbMATH DE Number: 4153800
zbMATH Keywords: singularly perturbed second order boundary value
zbMATH Keywords: discrete invariant embedding
zbMATH Keywords: Numerical results
zbMATH Keywords: retarding argument
reviewed by: John B. Butler jun.
MaRDI profile type: Publication
cites work: Q5677027
cites work: Introduction to the theory and application of differential equations with deviating arguments. Translated from the Russian by John L. Casti
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description: scientific article; zbMATH DE number 4153800