NUMERICAL SIMULATIONS OF THE DEGN-HARRISO MODEL IN THE NORMAL PARTIAL DISCRETE STATE: CASE 0 < α < 1

Abstract

Abstract: The goal of this study is to develop a numerical studies for the discrete fractional Lengyel-Epstein reaction-diffusion system as a examples of the chlorite-iodide-malonic-acid chemical reaction abbreviated as (CIMA) and Degn-Harriso model. Among the systems they represent is a model of pollu-tant migration in natural dispersed media where the aim of their studies are to determine the behavior of contaminants in heterogeneous porous media. To obtain stability analysis, the second-order centered difference approximation of the second derivative ∆u was applied, Eulers first order Taylor series method were taken into account. Besides, a numerical study testify the computational efficiency of the algorithms to the proposed model and present numerical results to verify the established analysis.AMS Mathematics Subject Classification : 65N06, 65N12, 65T50, 35R11.Key words and phrases : Discrete fractional, Reaction-diffusion, Finite difference method, Degn-Harriso model, Stability, Simulation.