A second-order fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation

We design a parameter robust fitted operator finite difference method for the numerical solution of a singularly perturbed delay parabolic partial differential equation. The method is constructed by replacing the classical differential operator with a fitted operator based on Crank-Nicolson's discretization. The proposed method is analysed for stability and convergence and it is found that this method is unconditionally stable and is convergent with order [image omitted], where k and h are respectively the time and space step sizes. The performance of this method is illustrated through a numerical example.