Numerical study of Burgers–Huxley equations via reduced differential transform method

Abstract

Burgers–Huxley equations and their reduced form are of vital importance in modeling the interaction between reaction mechanisms, convection effects and diffusion transports. In this paper, we applied the reduced form of differential transform method (reduced-DTM), present in previous works (Abazari and Borhanifar, Comput Math Appl 59:2711–2722, 2010; Borhanifar and Abazari, J Appl Math Comput 35:37–51, 2011; Borhanifar and Abazari, Opt Commun 283:2026–2031, 2010; Abazari and Ganji, Int J Comput Math 88(8):1749–1762, 2011; Abazari and Abazari, Commun Nonlinear Sci Numer Simul 17:619–629, 2012), to solving Burgers–Huxley equations and their three reduced equations, namely, the Burgers equation, the Huxley equation and the Burgers–Fisher equation. The results obtained employing RDTM are compared with previous semi-analytical methods, such as HPM (He, Appl Math Comput 135:73–79, 2003), HAM (Liao, Beyond perturbation: introduction to the homotopy analysis method. Chapman & Hall/CRC Press, Boca Raton, 2003), DTM (Zhou, Differential transformation and its application for electrical circuits. Huazhong University Press, Wuhan, 1986) and exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by classic HPM, HAM and DTM. The numerical results reveal that the RDTM is very effective, convenient and quite accurate to time dependance kind of nonlinear equations. It is predicted that the RDTM can be found widely applicable in engineering.