Second-order uniformly convergent numerical method for singularly perturbed delay parabolic partial differential equations

This article proposes a second-order uniformly convergent numerical method for singularly perturbed delay parabolic convection-diffusion equation having a regular boundary layer. To handle this layer phenomenon, the problem is solved on a priori special mesh by using the implicit-Euler scheme for the discretization of the time derivative and the upwind scheme for the spatial derivatives which results almost first-order convergence, that is, O(N−1ln⁡N+Δt). It is shown that, the implementation of Richardson extrapolation technique enhanced the order of convergence to O(N−2ln2⁡N+Δt2). To support the theoretical results, numerical experiments are carried out by applying the proposed technique on two test examples.