Fitted numerical scheme for singularly perturbed parabolic differential- difference with time lag

This paper deals with the numerical treatment of a singularly perturbed parabolic differential-difference equation with time delay. Taylor's series expansion is employed to approximate the terms with shift arguments in both spatial and time directions. The resulting problem is discretized using the implicit Euler method and fitted exponential cubic spline methods for time and space variables, respectively. The stability and uniform convergence of the proposed scheme are investigated. The scheme is proved to be uniformly convergent with the order of convergence $O(\Delta t +\ell<^>2)$O(Delta t+l2). A model test problem is considered to validate the applicability and efficiency of the scheme. It is observed that the proposed scheme provides more accurate results than methods available in the literature.