Numerical solution for singularly perturbed time-delayed parabolic problems involving two small parameters

Abstract

Here, we propose an upwind-based numerical technique for time-delayed parabolic convection- reaction-diffusion problems with two small parameters. Different layer-rectifying meshes are used in the spatial direction to handle the abrupt change in the solution due to the presence of perturbation parameters. For the 1D case, the Richardson extrapolation technique is used to elevate the accuracy of the upwind scheme. whereas in the case of 2D problems, the ADI-based operator-splitting algorithm is used which is computationally more robust