Application of Optimal Homotopy Asymptotic Method to Burger Equations

Nonlinear phenomena play a vital role in applied mathematics, physics, and engineering sciences. The Burger’s equation models efficiently certain problems of a fluid flow nature, in which either shocks or viscous dissipation is a significant factor. It can be used as a model for any nonlinear wave propagation problem subject to dissipation [1]. The first steadystate solutions of Burger equation were given by Young et al. [2] However, the equation gets its name from the extensive research of Burger’s [3]. The generalized Burger’s-Huxley introduced by Satsuma shows a prototype model for describing the communication among reaction mechanisms, convection effects, and diffusion transports [4]. Burger-Fisher equation has significant applications in various fields of applied mathematics and has physical applications such as gas dynamic, traffic flow, convection effect, and diffusion transport [5–12]. Marinca and Herişanu et al. introduced a new semianalytic method OHAM for approximate solution of nonlinear problems of thin filmflow of a fourth-grade fluid down a vertical cylinder. In progression of papers Marinca and Herişanu et al. have applied this method for the solution of nonlinear equations arising in the steady state flow of a fourth-grade fluid past a porous plate and for the solution of nonlinear equations arising in heat transfer [13–15]. The method has been applied by a number of researchers for solution of ordinary and partial differential equations [16– 21]. The motivation of this paper is to show the effectiveness of OHAM for the solution of Burger’s-Huxley and Burger’sFisher equations. We consider Burger’s-Huxley equation of the form