An Iterative Numerical Method for a Weakly Coupled System of Singularly Perturbed Convection–Diffusion Equations with Negative Shifts

In this paper, a numerical method based on an iterative scheme is proposed for a singularly perturbed weakly coupled system of delay differential equations of convection–diffusion type. In this method the solution of the delay problem is obtained as the limit of the solutions to a sequence of the non-delay problems. The numerical solutions of the non-delay problems are obtained by applying existing finite difference scheme for the non-delay weakly coupled system of singularly perturbed equations. An error estimate is derived by using maximum principle and in supremum norm. Numerical results illustrating the theory are also included.