An iterative numerical method for singularly perturbed reaction–diffusion equations with negative shift

In this paper, a numerical method based on an iterative scheme is proposed for a singularly perturbed delay differential equation of reaction–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 schemes and finite element method for the non-delay singularly perturbed equations. Error estimates are derived in the supremum norm. Numerical results illustrating the theory are also included.