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

被引：12

作者：

Chakravarthy, P. Pramod ^{[1
]}

Kumar, S. Dinesh ^{[1
]}

Rao, R. Nageshwar ^{[2
]}

机构：

[1] Visvesvaraya Natl Inst Technol, Dept Math, Nagpur 440010, Maharashtra, India

[2] VIT Univ, Sch Adv Sci, Vellore 632014, Tamil Nadu, India

来源：

AIN SHAMS ENGINEERING JOURNAL | 2017年 / 8卷 / 04期

关键词：

Singular perturbations; Boundary layer; Delay differential equation; Exponentially fitted finite difference method; BOUNDARY-VALUE-PROBLEMS; INITIAL-VALUE TECHNIQUE; SMALL SHIFTS; MIXED-TYPE; NUMERICAL TREATMENT;

D O I：

10.1016/j.asej.2015.09.004

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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. (C) 2015 Ain Shams University. Production and hosting by Elsevier B.V.

引用

页码：663 / 671

页数：9

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