Robust mid-point upwind scheme for singularly perturbed delay differential equations

In this paper, we consider singularly perturbed differential equations having delay on the convection and reaction terms. The considered problem exhibits boundary layer on the left or right side of the domain depending on the sign of the coefficient of the convection term. We approximated the terms containing the delay using Taylor series approximation. The resulting singularly perturbed boundary value problem is treated using exponentially fitted operator mid-point upwind finite difference method. The stability of the scheme is analysed and investigated using maximum principle and by constructing barrier functions for solution bound. We formulated the uniform converges of the scheme. The scheme converges uniformly with linear order of convergence. To validate the theoretical analysis and finding, we consider three examples exhibiting boundary layer on the left and right side of the domain. The obtained numerical result in this paper is accurate and parameter uniformly convergent.