Fitted Upwind Difference Scheme for Solving Singularly Perturbed Differential- Difference Equations with Negative Shift

In this paper, a fitted upwind difference scheme has been presented for solving singularly perturbed differential-difference equations with negative shift. First, the singularly perturbed differential-difference equation has been replaced by an asymptotically equivalent singular perturbation problem. Then, a fitting factor is introduced into upwind finite difference scheme and obtained from the theory of singular perturbations. Then, a three term recurrence relation is obtained. The resulted tri diagonal system has been solved by Discrete Invariant Imbedding Algorithm. The efficiency of the method has been demonstrated by implementing on several model examples by taking different values for the delay and the perturbation parameters.