An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion-reaction problem with two small parameters

The manuscript contemplates a computationally robust numerical algorithm for the solution of a singularly perturbed 2D time-delayed parabolic convection-diffusion-reaction problem involving two small parameters. The operator-splitting algorithm on a uniform mesh is used in the time direction. To handle the abrupt change in the solution due to the presence of perturbation parameters, the upwind scheme is used in the spatial direction on a layer-rectifying mesh, namely, the Shishkin mesh. This makes the accuracy in space to be one (with a logarithmic term). The use of Bakhvalov-Shishkin mesh in the spatial domain rectifies this logarithmic effect on the rate of convergence. The highly efficient Thomas algorithm is used for the computation. The devised method is claimed to be parameter uniform and globally first-order accurate. All the theoretical claims are corroborated in practice with valid numerical tests.