Document Type : Research Articles

Authors

1 Department of Applied Mathematics, Adama Science and Technology University

2 Department to Mathematics, Jimma University, Jimma, Ethiopia

10.22080/cjms.2020.19425.1547

Abstract

In this paper, singularly perturbed differential equations having delay on the convection and reaction terms are considered. The highest order derivative term in the equation is multiplied
by a perturbation parameter \epsilon taking arbitrary values in the interval (0; 1]. For small \epsilon, the problem involves a boundary layer on
the left or right side of the domain depending on the sign of the
coefficient of the convective term. The terms involving the delay
are approximated using Taylor series approximation. The resulting
singularly perturbed boundary value problem is treated using exponentially fitted upwind finite difference method. The stability of
the proposed scheme is analysed and investigated using maximum
principle and barrier functions for solution bound. The formulated
scheme converges independent of the perturbation parameter with
rate of convergence O(N−1). Richardson extrapolation technique is
applied to accelerate the rate of convergence of the scheme to order
O(N−2). To validate the theoretical finding, three model examples
having boundary layer behaviour are considered. The maximum
absolute error and rate of convergence of the scheme are computed.
The proposed scheme gives accurate and parameter uniformly convergent result.

Keywords