Numerical solution of singular perturbation problems
type: Item
instance of: scholarly article
title: Numerical solution of singular perturbation problems
zbMATH Open document ID: 0819.65113
DOI: 10.1007/BF02575883
author: Donato Trigiante
author: Francesca Mazzia
published in: Calcolo
publication date: 1995-03-30T00:00:00Z
review text: This paper deals with the solution of the boundary value problem \(\varepsilon y'' + s(t)y' + c(t)y = f(t)\), \(t \in [t_{\min}, t_{\max}]\), \(y(t_{\min}) = a\), \(y(t_{\max}) = b\), where \(\varepsilon\) is positive (it could be very small), \(c(t)\) and \(f(t)\) are continuous functions on the integration interval \([t_{\min}, t_{\max}]\), and \(s(t)\) is differentiable. The presented method is based on second order difference schemes where the convergence is not very fast. It applies a mesh selection strategy derived by using sufficient conditions which ensure the well-conditioning of the corresponding tridiagonal matrices. It has the positive feature of choosing the initial mesh very efficiently and this allows it to perform better than higher order methods, especially for small values of \(\varepsilon\) or for not very high tolerance. Numerical tests are reported.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 739150
zbMATH Keywords: singular perturbation
zbMATH Keywords: numerical examples
zbMATH Keywords: second order difference schemes
zbMATH Keywords: convergence
zbMATH Keywords: mesh selection strategy
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 739150