Accelerated nonstandard finite difference method for solving singularly perturbed parabolic reaction diffusion problem.

Abstract

In this study, accelerated nonstandard finite difference method is presented for solving singularly perturbed parabolic reaction diffusion initial boundary value problems. Richardson extrapolation technique applied to improve accuracy of the solution and accelerates its rate of convergence from second-order to fourth-order and fourth-order to sixth-order. The consistency and stability of the proposed method have been established very well to guarantee to the convergence of the method. Model examples were considered to illustrate conformation of the theoretical description with experimentation results. The numerical experimentation is carried out some model problems and both the results are presented in tables and graphs. The present method is stable, convergent and gives more accurate solution than some methods existing the literature