Solutions Of Nonlinear Partial Differential Equations By Homotopy Analysis Method

In this dissertation, some topics are described, including mathematical mechanization, the AC=BD model theory put forward by Prof. Zhang Hongqing, and analytical approximate methods for solving nonlinear equations. Under the guidance of Homtopy Analysis Method, some K(m,n) equations and Zakharov-Kuznetsov equation are solved. The comparison between the HAM approximation solution and the exact solution shows that we successfully solve these equations by HAM. In this paper, the main work is done as follows:Chapter 1. The development of mathematical physics mechanization and analytical approximate methods for solving nonlinear equations is introduced. We give an introduction of mathematical physics mechanization at home and abroad in summary. At last,the outline of this dissertation is given.Chapter 2. The construction of transformation of differential equation(s) is concerned under the uniform frame work of AC=BD model. The basic theory of C-D pair is presented.Chapter 3. We describe the HAM's basic idea and its advantage in solving nonlinear equations. Then the relationship between HAM and other analytical approximate methods is discussed.Chapter 4. Under the guidance of Homtopy Analysis Method, some K(m,n) equations and Zakharov-Kuznetsov equation are solved. At last we analyze the error between the HAM approximation solutions and the exact solutions.