Parameter uniform numerical method for a singularly perturbed boundary value problem for a linear system of parabolic second order delay differential equations

Parthiban Saminathan; Valarmathi Sigamani; Franklin Victor

doi:10.26637/MJM0702/0004

Abstract

A singularly perturbed boundary value problem for a linear system of two parabolic second order delay differential equations of reaction-diffusion type is considered. As the highest order space derivatives are multiplied by singular perturbation parameters, the solution exhibits boundary layers. Also, the delay term that occurs in the space variable gives rise to interior layers. A numerical method which uses classical finite difference scheme on a Shishkin piecewise uniform mesh is suggested to approximate the solution. The method is proved to be first order convergent uniformly for all the values of the singular perturbation parameters. Numerical illustrations are
presented so that the theoretical results are supported.

Keywords:

Singular perturbation problems, boundary layers, parabolic delay-differential equations, finite difference scheme, Shishkin mesh, parameter uniform convergence

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Parthiban Saminathan Department of Mathematics, Bishop Heber College, Tiruchirappalli-620 017, Tamil Nadu, India.
Valarmathi Sigamani Department of Mathematics, Bishop Heber College, Tiruchirappalli-620 017, Tamil Nadu, India.
Franklin Victor Department of Mathematics, Bishop Heber College, Tiruchirappalli-620 017, Tamil Nadu, India.

Pages: 147-160
Date Published: 01-04-2019
Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)

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