Application Of Homotopy Perturbation Method To Solve Nonliear Differential Equation

Nonlinear phenomena appear in various fields of modern science and technology, whose mathematical model is usually described by nonlinear equations, and thus solving non-linear equations has important theoretical and practical significance. In recent years ,a new approximate analytic solution method for nonlinear equations is proposed in some papers by combining the homotopy theory with the perturbation method , namely the homotopy perturbation method.The essence of the homotopy perturbation method to solve problems lies in to change the complicated nonlinear problem into several simple linear problems to deal with.This paper applied homotopy perturbation method to solve nonlinear equations from two aspects.1.Some approximate solutions of nonlinear ordinary differential equations were achieved,including a burning equation, Rayleigh equation and nonlinear boundary problem.2.Some approximate solutions of nonlinear partial differential equations achieved,including nonlinear advection equation, nonlinear wave equation and Fisher equation.This paper worked fully to demonstrate the homotopy perturbation method some notable features, such as not dependent on nonlinear equation of small parameter and the initial guess solution can be freely choosen, etc.The method has the characteristics of convenient operation, suitability, high flexibility for solving nonlinear problem.