Robust Finite Difference Method for Singularly Perturbed Two-Parameter Parabolic Convection-Diffusion Problems

Robust finite difference method is introduced in order to solve singularly perturbed two parametric parabolic convection-diffusion problems. In order to discretize the solution domain, Micken's type discretization on a uniform mesh is applied and then followed by the fitted operator approach. The convergence of the method is established and observed to be first-order convergent, but it is accelerated by Richardson extrapolation. To validate the applicability of the proposed method, some numerical examples are considered and observed that the numerical results confirm the agreement of the method with the theoretical results effectively. Furthermore, the method is convergent regardless of perturbation parameter and produces more accurate solution than the standard methods for solving singularly perturbed parabolic problems.

Automated summary

The study introduces a robust finite difference method for solving singularly perturbed parabolic convection-diffusion problems, demonstrating its convergence and effectiveness through numerical examples. The method is shown to be more accurate and convergent regardless of perturbation parameter compared to standard methods for solving parabolic problems.