A uniformly convergent finite difference scheme for Robin type singularly perturbed parabolic convection diffusion problem

摘要

In this paper, a second order numerical scheme for solving a singularly perturbed convection diffusion problem with Robin boundary conditions is proposed. The numerical scheme is a combination of the fitted operator finite difference and the backward Euler finite difference methods. These are designed in order to solve respectively the spatial derivatives and the time derivative. Using some properties of the discrete problem the methods are analysed for convergence. Richardson extrapolation technique is used to improve the accuracy and also accelerate the convergence of the method. Numerical simulations are carried out to confirm the theoretical findings in the analysis before and after extrapolation.