The Application Of Homotopy Analysis Method And Pade Approximation In The Nonlinear Dynamic System

In recent years,the emergence of a variety of nonlinear problems have emerged in mathematics,physics,chemistry,biology,medicine,economics,engineering,cybernetics and many other scientific fields.In the process of solving these problems,the theory and method produced by the modern mathematics is very import,ant,in which,including Meklnikov method,multi-scale method and homotopy analysis method.These methods have become an effective tool for solving nonlinear problems in the field of science and technology.In addition,with the rapid development of electronic technology,polynomial approximation has been rapidly developed and widely used.The purpose of approxi-mation is a simple function to approximate more complex functions,polynomial is an approximation of common tools.Although the polynomial is a good approximation func-tion,however,for some singular functions,polynomial approximation can not achieve good approximation results.Polynomial pade approximation is a generalization,which can achieve good results near the poles.This paper studies the application of the homotopy analysis method and polynomial pade approximation theory in nonlinear systems,for solving some nonlinear problem,first,based on the homotopy analysis method to compute the approximate analytic so-lution of nonlinear system,homotopy analysis method provides an effective method to adjust and control the convergence of the series solutions,the computational efficiency is improved.Then,we can obtain the[m,n]order solution of the analysis solution,so,we achieve the approximate analytical solutions of the homotopy solution.By solving the nonlinear system,we can find the approximate solution of the homotopy analysis is more effective than the homotopy analysis solutions.