A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

In this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1]. The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference s...

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Main Authors:	Ishwariya Raj, Princy Mercy Johnson, John J.H Miller, Valarmathi Sigamani
Format:	Article
Language:	English
Published:	Biomath Forum 2016-09-01
Series:	Biomath
Subjects:	Singular Perturbation Problems, boundary layers, nonlinear differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence.
Online Access:	http://www.biomathforum.org/biomath/index.php/biomath/article/view/573

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spelling	doaj-546f02b729304107a7795416c03e951b2020-11-24T20:44:06ZengBiomath ForumBiomath1314-684X1314-72182016-09-015210.11145/j.biomath.2016.08.111532A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equationsIshwariya Raj0Princy Mercy Johnson1John J.H Miller2Valarmathi Sigamani3Bishop Heber College, Tiruchirappalli-620017 Tamil Nadu, IndiaBishop Heber College, Tiruchirappalli-620017 Tamil Nadu, IndiaInstitute for Numerical Computation and Analysis, DublinBishop Heber College, Tiruchirappalli-620017 Tamil Nadu, IndiaIn this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1]. The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be almost first order convergent in the maximum norm uniformly in the perturbation parameters.http://www.biomathforum.org/biomath/index.php/biomath/article/view/573Singular Perturbation Problems, boundary layers, nonlinear differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Ishwariya Raj Princy Mercy Johnson John J.H Miller Valarmathi Sigamani
spellingShingle	Ishwariya Raj Princy Mercy Johnson John J.H Miller Valarmathi Sigamani A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations Biomath Singular Perturbation Problems, boundary layers, nonlinear differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence.
author_facet	Ishwariya Raj Princy Mercy Johnson John J.H Miller Valarmathi Sigamani
author_sort	Ishwariya Raj
title	A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations
title_short	A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations
title_full	A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations
title_fullStr	A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations
title_full_unstemmed	A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations
title_sort	parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations
publisher	Biomath Forum
series	Biomath
issn	1314-684X 1314-7218
publishDate	2016-09-01
description	In this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1]. The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be almost first order convergent in the maximum norm uniformly in the perturbation parameters.
topic	Singular Perturbation Problems, boundary layers, nonlinear differential equations, finite difference schemes, Shishkin mesh, parameter uniform convergence.
url	http://www.biomathforum.org/biomath/index.php/biomath/article/view/573
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A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

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