A domain decomposition method for solving singularly perturbed parabolic reaction-diffusion problems with time delay

We design and analyse a domain decomposition method for solving, singularly perturbed parabolic reaction-diffusion problems with time delay. Using the asymptotic behavior of the solution, we decompose the original domain of the problem into three overlapping subdomains, two of which are boundary layer subdomains and one is a regular subdomain. On each subdornain, we discretize the problem by the backward Euler scheme in the time direction and the central difference scheme in the spatial direction. The proposed method is shown to be uniformly convergent, having almost second order in space and first order in time. In addition, we prove that the proposed method converges much faster for small values of perturbation parameter epsilon. At the end, some numerical results are given in support of theoretical findings.