A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem

In this article, we consider a class of singularly perturbed two-parameter parabolic partial differential equations with time delay on a rectangular domain. The solution bounds are derived by asymptotic analysis of the problem. We construct a numerical method using a hybrid monotone finite difference scheme on a rectangular mesh which is a product of uniform mesh in time and a layer-adapted Shishkin mesh in space. The error analysis is given for the proposed numerical method using truncation error and barrier function approach, and it is shown to be almost second- and first-order convergent in space and time variables, respectively, independent of both the perturbation parameters. At the end, we present some numerical results in support of the theory.