This article presents a higher-order parameter uniformly convergent method for a singularly perturbed delay parabolic reaction-diffusion initial-boundary-value problem. For the discretization of the time derivative, we use the Crank-Nicolson scheme on the uniform mesh and for the spatial discretization, we use the central difference scheme on the Shishkin mesh, which provides a second order convergence rate. To enhance the order of convergence, we apply the Richardson extrapolation technique. We prove that the proposed method converges uniformly with respect to the perturbation parameter and also attains almost fourth order convergence rate. Finally, to support the theoretical results, we present some numerical experiments by using the proposed method.
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Singular perturbation, Delay parabolic problems, Crank-Nicolson scheme, Richardson extrapolation.