Numerical simulation of the generalized Huxley equation by He's homotopy perturbation method

In this paper, the solution of the generalized Huxley equation is obtained by means of homotopy perturbation method and Adomian decomposition method. The comparison reveals that the former method is more effective than the later. In this method, a homotopy is constructed for the equation.The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Moreover, we will show that He's homotopy perturbation method overcome the difficulties arising in calculating Adomian polynomials. It is predicted that the HPM can be found wide application in engineering problems.