The Further Discussion For Homotopy Analysis Method And Their Modification

Homotopy Analysis Method.is more efficient for a lot of nonlinear problems.This paper will introduce the method with five chapters.Firstly,Take the simple problems with the work for instance,the paper will describe the basic idea of the Homotopy Analysis Method roundly,then,show its effectiveness and flexibility.Secondly,the paper will discuss the relation between Homotopy Analysis Method and the traditional analytical method,aMoilernd point out that they are particular cases of Homotopy Analysis Method.Thirdly,the paper will expound that the HAM provides us with great freedom to replace a nonlinear differential equation of order n into an infinite number of linear differential equations of order k,where the order k is even unnecessary to be equal to the order n.Finally,the paper will modify the HAM for solving nonhomogeneous differential equations. The main advantage of the modified HAM is that we can accelerate the convergence rate,minimize iterative times,accordingly,save the computation time and evaluate the efficiency, if we choose the proper decomposition for the nonhomogeneous term in the modified HAM.Examples showed the capability of the modified HAM. expansion method,nonhomogeneous.differential equations.