On the Exact Solution of Burgers-Huxley Equation Using the Homotopy Perturbation Method

The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence towards the exact solutions of HPM is numerically shown. Results show that the HPM is efficient method with acceptable accuracy to solve the Burgers-Huxley equation. Also, the results prove that the method is an efficient and powerful algorithm to construct the exact solution of non-linear differential equations.

Cite this paper

Nourazar, S. , Soori, M. and Nazari-Golshan, A. (2015) On the Exact Solution of Burgers-Huxley Equation Using the Homotopy Perturbation Method. Journal of Applied Mathematics and Physics, 3, 285-294. doi: 10.4236/jamp.2015.33042.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] He, J.H. (1999) Homotopy Perturbation Technique. Computer Methods in Applied Mechanics and Engineering, 178, 257-262. http://dx.doi.org/10.1016/S0045-7825(99)00018-3 [2] He, J.H. (2005) Application of Homotopy Perturbation Method to Nonlinear Wave Equations. Chaos Solitons & Fractals, 26, 695-700. http://dx.doi.org/10.1016/j.chaos.2005.03.006 [3] Nourazar, S.S., Soori, M. and Nazari-Golshan, A. (2011) On the Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method. Australian Journal of Basic and Applied Sciences, 5, 1400-1411. [4] Krisnangkura, M., Chinviriyasit, S. and Chinviriyasit, W. (2012) Analytic Study of the Generalized Burger’s-Huxley Equation by Hyperbolic Tangent Method. Applied Mathematics and Computation, 218, 10843-10847.http://dx.doi.org/10.1016/j.amc.2012.04.044 [5] Gao, H. and Zhao, R.X. (2010) New Exact Solutions to the Generalized Burgers-Huxley Equation. Applied Mathematics and Computation, 217, 1598-1603. http://dx.doi.org/10.1016/j.amc.2009.07.020 [6] Hashim, I., Noorani, M.S.M. and Said Al-Hadidi, M.R. (2006) Solving the Generalized Burgers-Huxley Equation Using the Adomian Decomposition Method. Mathematical and Computer Modelling, 43, 1404-1411.http://dx.doi.org/10.1016/j.mcm.2005.08.017 [7] Wang, X.Y., Zhu, Z.S. and Lu, Y.K. (1990) Solitary Wave Solutions of the Generalised Burgers-Huxley Equation. Journal of Physics A: Mathematical and General, 23, 271. http://dx.doi.org/10.1088/0305-4470/23/3/011 [8] Darvishi, M.T., Kheybari, S. and Khani, F. (2008) Spectral Collocation Method and Darvishi’s Preconditionings to Solve the Generalized Burgers-Huxley Equation. Communications in Nonlinear Science and Numerical Simulation, 13, 2091-2103. http://dx.doi.org/10.1016/j.cnsns.2007.05.023 [9] Satsuma, J. (1987) Topics in Soliton Theory and Exactly Solvable Nonlinear Equations. World Scientific, The Singapore City. [10] Wang, X.Y. (1985) Nerve Propagation and Wall in Liquid Crystals. Physics Letters A, 112, 402-406.http://dx.doi.org/10.1016/0375-9601(85)90411-6 [11] Whitham, G.B. (1974) Linear and Nonlinear Waves. Wiley, New York. [12] Deng, X.J. (2008) Travelling Wave Solutions for the Generalized Burgers-Huxley Equation. Applied Mathematics and Computation, 204, 733-737. http://dx.doi.org/10.1016/j.amc.2008.07.020