A robust method of lines solution for singularly perturbed delay parabolic problem

A numerical method is proposed to solve a non-autonomous singularly perturbed parabolic differential equation with a time delay. The solution is obtained by a step by step discretisation process. First the spatial derivatives are discretised via a fitted operator finite difference scheme and then analysed for convergence. The Crank Nicolson finite difference scheme is used to solve the resulting system of initial value problem and also analysed for convergence. Using Richardson extrapolation approach, the accuracy of fitted operator finite difference scheme is improved into a second order. Numerical results are presented to support the theoretical findings.