Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem

Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem

<p/> <p>We consider a singularly perturbed one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. The monotone operator is combined with the piecewise uniform Shishkin-type meshes. We show that the scheme is second-order convergent, in...

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Main Author: &#199;ak&#305;r Musa
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Advances in Difference Equations
Online Access:http://www.advancesindifferenceequations.com/content/2010/102484
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spelling doaj-1cfd66dbc82a49acb5d24a541c9d25d02020-11-24T22:00:04ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-0120101102484Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem&#199;ak&#305;r Musa<p/> <p>We consider a singularly perturbed one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. The monotone operator is combined with the piecewise uniform Shishkin-type meshes. We show that the scheme is second-order convergent, in the discrete maximum norm, independently of the perturbation parameter except for a logarithmic factor. Numerical examples support the theoretical results.</p> http://www.advancesindifferenceequations.com/content/2010/102484
collection DOAJ
language English
format Article
sources DOAJ
author &#199;ak&#305;r Musa
spellingShingle &#199;ak&#305;r Musa
Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem
Advances in Difference Equations
author_facet &#199;ak&#305;r Musa
author_sort &#199;ak&#305;r Musa
title Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem
title_short Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem
title_full Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem
title_fullStr Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem
title_full_unstemmed Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem
title_sort uniform second-order difference method for a singularly perturbed three-point boundary value problem
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1839
1687-1847
publishDate 2010-01-01
description <p/> <p>We consider a singularly perturbed one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. The monotone operator is combined with the piecewise uniform Shishkin-type meshes. We show that the scheme is second-order convergent, in the discrete maximum norm, independently of the perturbation parameter except for a logarithmic factor. Numerical examples support the theoretical results.</p>
url http://www.advancesindifferenceequations.com/content/2010/102484
work_keys_str_mv AT 199ak305rmusa uniformsecondorderdifferencemethodforasingularlyperturbedthreepointboundaryvalueproblem
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