Numerical algorithm for singularly perturbed delay differential equations with layer and oscillatory behavior

We consider the numerical approximation of singularly perturbed linear second order reaction-diffusion boundary value problems with a small shift(δ) in the undifferentiated term and the shift depends on the small parameter(ǫ). The presence of small parameter induces twin boundary layers. The problem is discretized using standard finite difference scheme on an uniform mesh and the retarded arguments are interpolated/extrapolated using the known computational grid points. We present a new algorithm to interpolate/exptrapolate the retarded term in terms of its neighbouring points. The scheme is proved to be stable and the error estimate is also given. It is shown that the shift has significant effect on the behavior of the solution. Numerical experiments are performed to support both the theoretical results as well as the existing results in the literature. AMS Subject Classification. 34K28, 65N06, 65N12