Third-Order Approximate Solution of Chemical Reaction-Diffusion Brusselator System Using Optimal Homotopy Asymptotic Method

Salem Alkhalaf

doi:10.1155/2017/3895701

Abstract

The objective of this paper is to investigate the effectiveness and performance of optimal homotopy asymptotic method in solving a system of nonlinear partial differential equations. Since mathematical modeling of certain chemical reaction-diffusion experiments leads to Brusselator equations, it is worth demanding a new technique to solve such a system. We construct a new efficient recurrent relation to solve nonlinear Brusselator system of equations. It is observed that the method is easy to implement and quite valuable for handling nonlinear system of partial differential equations and yielding excellent results at minimum computational cost. Analytical solutions of Brusselator system are presented to demonstrate the viability and practical usefulness of the method. The results reveal that the method is explicit, effective, and easy to use.

Highlights

The Brusselator model, the nonlinear system of partial differential equations, arises in the modeling of certain chemical reaction-diffusion processes
The objective of this paper is to investigate the effectiveness and performance of optimal homotopy asymptotic method in solving a system of nonlinear partial differential equations
A pair of variables are involved in dealing with these chemical reactions; intermediates with input and output chemicals, whose concentrations are likely to be controlled during the reaction process, are substantial under quite genuine conditions and are discussed by Nicolis and Prigogine in [2, 3]

Summary

Introduction

The Brusselator model, the nonlinear system of partial differential equations, arises in the modeling of certain chemical reaction-diffusion processes. This Brusselator reactiondiffusion model plays a substantial role in the study of cooperative processes of chemical kinetics This system occurs in a large number of physical problems. A pair of variables are involved in dealing with these chemical reactions; intermediates with input and output chemicals, whose concentrations are likely to be controlled during the reaction process, are substantial under quite genuine conditions and are discussed by Nicolis and Prigogine in [2, 3]. This model has been revealed as the trimolecular model [4]

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Results

Conclusion