HOMOTOPY ANALYSIS AND PADE METHODS FOR SOLVING TWO NONLINEAR EQUATIONS

In this paper, we are giving analytic approximate solutions to nonlinear PDEs using the Homotopy Analysis Method (HAM) and Homotopy Pad´e Method(HPad´eM). The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence regions of solution series. It is illustrated that HPad´eM accelerates the convergence of the related series. The results reveal these methods are remarkably effective.