An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays

This paper deals with singularly perturbed boundary value problem for a linear second order delay differential equation. It is known that the classical numerical methods are not satisfactory when applied to solve singularly perturbed problems in delay differential equations. In this paper we present...

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Main Authors:	P. Pramod Chakravarthy, S. Dinesh Kumar, R. Nageshwar Rao
Format:	Article
Language:	English
Published:	Elsevier 2017-12-01
Series:	Ain Shams Engineering Journal
Subjects:	Singular perturbations Boundary layer Delay differential equation Exponentially fitted finite difference method
Online Access:	http://www.sciencedirect.com/science/article/pii/S2090447915001574

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spelling	doaj-a5125ef8bde64824b7917c507b347be22021-06-02T03:34:25ZengElsevierAin Shams Engineering Journal2090-44792017-12-018466367110.1016/j.asej.2015.09.004An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delaysP. Pramod Chakravarthy0S. Dinesh Kumar1R. Nageshwar Rao2Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, IndiaDepartment of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, IndiaSchool of Advanced Sciences, VIT University, Vellore, Tamil Nadu 632014, IndiaThis paper deals with singularly perturbed boundary value problem for a linear second order delay differential equation. It is known that the classical numerical methods are not satisfactory when applied to solve singularly perturbed problems in delay differential equations. In this paper we present an exponentially fitted finite difference scheme to overcome the drawbacks of the corresponding classical counter parts. The stability of the scheme is investigated. The proposed scheme is analyzed for convergence. Several linear singularly perturbed delay differential equations have been solved and the numerical results are presented to support the theory.http://www.sciencedirect.com/science/article/pii/S2090447915001574Singular perturbationsBoundary layerDelay differential equationExponentially fitted finite difference method
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	P. Pramod Chakravarthy S. Dinesh Kumar R. Nageshwar Rao
spellingShingle	P. Pramod Chakravarthy S. Dinesh Kumar R. Nageshwar Rao An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays Ain Shams Engineering Journal Singular perturbations Boundary layer Delay differential equation Exponentially fitted finite difference method
author_facet	P. Pramod Chakravarthy S. Dinesh Kumar R. Nageshwar Rao
author_sort	P. Pramod Chakravarthy
title	An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays
title_short	An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays
title_full	An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays
title_fullStr	An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays
title_full_unstemmed	An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays
title_sort	exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays
publisher	Elsevier
series	Ain Shams Engineering Journal
issn	2090-4479
publishDate	2017-12-01
description	This paper deals with singularly perturbed boundary value problem for a linear second order delay differential equation. It is known that the classical numerical methods are not satisfactory when applied to solve singularly perturbed problems in delay differential equations. In this paper we present an exponentially fitted finite difference scheme to overcome the drawbacks of the corresponding classical counter parts. The stability of the scheme is investigated. The proposed scheme is analyzed for convergence. Several linear singularly perturbed delay differential equations have been solved and the numerical results are presented to support the theory.
topic	Singular perturbations Boundary layer Delay differential equation Exponentially fitted finite difference method
url	http://www.sciencedirect.com/science/article/pii/S2090447915001574
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An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays

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