Analytical Treatment of Generalized Burgers-Huxley Equation by Homotopy Analysis Method

Abstract. In this paper, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the generalized Burgers-Huxley and Huxley equations. The series solution is developed and given explicitly. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. The comparison of the HAM results with the variational iteration method (VIM) results is made. It is shown, in particular, that the VIM solutions are only special cases of the HAM solutions