Hybrid method for numerical solution of singularly perturbed delay differential equations

This paper is concerned with the numerical technique for a singularly perturbed second-order differential–difference equation of the convection–diffusion type with small delay parameter δ   whose solution has a single boundary layer. We analyse three difference operators LkN, k = 1, 2, 3 a simple upwind scheme, midpoint upwind scheme and a hybrid scheme, respectively, on a Shishkin mesh to approximate the solution of the problem. The hybrid algorithm uses central difference in the boundary layer region and midpoint upwind scheme outside the boundary layer. We have concluded that the hybrid scheme gives better accuracy. The paper concludes with a few numerical results exhibiting the performance of these three schemes.