Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior

We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, into subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree and determined Bezier curves on any subinterval by control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems.