Analysis of a Hybrid Numerical Scheme for Singularly Perturbed Convection-Diffusion Type Delay Problems.

In this paper, a class of singularly perturbed delay differential equations of convection-diffusion (C–D) type is considered. The solutions for these problems exhibit boundary as well as interior layer due to the presence of delay. A few a priori estimates are given on the exact solution and its derivatives. We propose a numerical technique consisting of hybrid finite difference scheme on a Shishkin-type mesh. The proposed technique is analyzed for its consistency, stability and convergence. To show the effectiveness of the present approach, we conduct some numerical experiments. An almost second-order -uniform convergence is established. [ABSTRACT FROM AUTHOR]