1 The Variational Iteration Method and the Homotopy Perturbation Method to the Exact Solution of the generalized Burgers-Fisher Equation By: Mohsen Soori University: Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran Date: 21 July 2018 Composition of the Jury: Prof. S. Salman Nourazar Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic) Dr. Akbar Nazar-Golshan Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic) Abstract: The exact solution of Burgers-Fisher equation is obtained by using the Variational Iteration Method (VIM) and the Homotopy Perturbation Method (HPM). To present accuracy as well as reliability of the methods in finding the exact solution of the equation, a comparison is also made between obtained results. The study proves that the methods are effective and powerful algorithms with acceptable accuracy in order to obtain the exact solution of Burgers-Fisher equation as a non-linear differential equation. Keywords: Burgers-Fisher equation, Variational Iteration Method, Homotopy Perturbation Method, Nonlinear differential equations 1. Introduction In order to describe behavior and effects of many phenomena in the different field of science as well as engineering, the functional equations such as linear and nonlinear partial differential equations, integral and integro-differential equations and stochastic equations are used. The investigation for the exact solutions of nonlinear partial differential equations plays an important role in the study of nonlinear physical phenomena. Most of the equations do not have analytical solution which can be handled by semi-analytical methods. To obtain exact solution of nonlinear differential equations, semi-analytical methods such as the Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM) can be considered. They are powerful algorithms in solving various kinds of linear and nonlinear equations. The ideas of the VIM and HPM were first pioneered by He [1,2]. In order to solve autonomous ordinary differential equation as well as delay differential equation, the VIM is applied by He [3,4]. Also, application of the HPM in solving the non-linear non-homogeneous partial differential equations is presented by He [5]. The homotopy perturbation method is used by Nourazar et al. [6-8] in order to obtain exact solution of nonlinear differential equations. Application of the Variational Iteration Method and the Homotopy Perturbation Method to the Fisher Type Equation is presented by Soori et al. [9]. To solve Burgers‐Fisher equation, new implementation of radial basis functions is presented by Tatari et al. [10]. Also, Zhao et al. [11] presented application of Chebyshev–Legendre pseudo-spectral method to the generalised Burgers–Fisher equation. The investigation into the exact solutions of the generalized time-delayed Burgers–Fisher equation with positive fractional power terms is presented by Zhang et al. [12]. The Burgers-Fisher equation is uncovered by Johannes Martinus Burgers and Ronald Aylmer Fisher. Behaviors of many physical systems encountered in modeling of various mechanisms lead to the generalized Burgers–