Fitted scheme for singularly perturbed time delay reaction-diffusion problems

Abstract

In this article, we constructed a numerical scheme for singularly perturbed time-delay reaction-diffusion problems. For the discretization of the time derivative, we used the Crank-Nicolson method and a hybrid scheme, which is a combination of the fourth-order compact difference scheme and the cen-tral difference scheme on a special type of Shishkin mesh in the spatial di-rection. The proposed scheme is shown to be second-order accurate in time and fourth-order accurate with a logarithmic factor in space. The uniform convergence of the proposed scheme is discussed. Numerical investigations are carried out to demonstrate the efficacy and uniform convergence of the proposed scheme, and the obtained numerical results reveal the better per-formance of the present scheme, as compared with some existing methods in the literature.

Keywords

• singular perturbation
• time-delay, parabolic differential equa-tion, reaction-diffusion problem, hybrid scheme