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

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Authors :

Parthiban Saminathan 1 , Valarmathi Sigamani 2 * and Franklin Victor 3

Author Address :

1,2,3 Department of Mathematics, Bishop Heber College, Tiruchirappalli-620 017, Tamil Nadu, India.

*Corresponding author.

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.

DOI :

10.26637/MJM0702/0004

Article Info :

Received : October 18, 2018; Accepted : March 14, 2019.

 

 

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