A method of line with improved accuracy for singularly perturbed parabolic convection–diffusion problems with large temporal lag

A robust numerical scheme is proposed to solve singularly perturbed large time-delay parabolic convection–diffusion problems. For domain discretization, the backward-Euler method for the time derivative and Micken’s type discretization for the space derivatives are used. Using a Richardson extrapolation technique the ɛ-uniform accuracy of the method is improved to second order convergences. We present numerical examples to confirm the agreement of the numerical methods with the theoretical results. The proposed numerical scheme is parameter-uniform convergent, more accurate and robust.