An efficient numerical approach for singularly perturbed parabolic convection-diffusion problems with large time-lag

In this paper, an efficient finite difference method is presented for solving singularly perturbed linear second order parabolic problems with large time lag. The comparable numerical model is related to automatically controlled system with spatial diffusion of reactants  in the processes. This study focuses on the formation of boundary layer behavior or oscillatory behaviors due to the presence of delay parameters and perturbation parameter. The numerical scheme comprising an exponentially fitted spline based difference scheme on a uniform mesh supported by Crank-Nicolson Method is constructed. It is found that the present method converges with second order accurate in both temporal and spatial variables. The convergence analysis and running time of the program with varied grid sizes are then used to do the efficiency analysis. The proposed scheme  accuracy and efficiency are also demonstrated through numerical experiments.