Accelerated Non-Standard Finite Difference Method for Singularly Perturbed Reaction -Diffusion Boundary Value Problems.

Abstract

In this study, accelerated non-standard finite difference method is presented for solving singularly perturbed reaction-diffusion boundary value problems. Richardson extrapolation technique helps to improve accuracy of the solution and accelerates its rate of convergence from second order to fourth order. Consistency and stability of the present method established very well to guarantee the convergence of the method. Model examples were considered to illustrate the conformation of theoretical description with experiential results. In a net shell, the presented method is formulated for the class of singularly perturbed reaction- diffusion boundary value problems which is stable, convergent and gives more accurate solution than some methods existing in the literature.