Accelerated fitted operator finite difference method for singularly perturbed parabolic reaction-diffusion problems

Abstract

This paper deals with the numerical treatment of singularly perturbed parabolic reaction-diffusion initial boundary value problems. Introducing a fitting parameter into the asymptotic solution and applying average finite difference approximation, a fitted operator finite difference method is developed for solving the problem. To accelerate the rate of convergence of the method, the Richardson extrapolation technique is applied. The consistency and stability of the proposed method have been established very well to ensure the convergence of the method. Numerical experimentation is carried out on some model problems and the results are presented both in tables and graphs. The numerical results are compared with the findings of some methods existing in the literature and found to be more accurate. Generally, the formulated method is consistent, stable, and more accurate than some methods existing in the literature for solving singularly perturbed parabolic reaction-diffusion initial boundary value problems.