Solving A Class Of Difference Equations By Using Difference Characteristic Column Method

In modern times, with the development of science and technology and economy,the nonlinear difference equations are used in statistical problems, biology, genetics, medicine, geometry, mechanics, economics and population dynamics, and many other fields widely. Further more, it could be used to solve various real problems.So the study that the exact solutions of nonlinear difference equations is crucial.In recent years, Wu’s characteristic set method becomes a new method for solving the exact solutions of difference equations. By the study of the characteristic set method the reduction and exact solutions of the nonlinear difference equations will be obtained.This thesis is divided into three chapters:In the first chapter, we introduce the production and development of the mathematics mechanization at first. And then the production and application of the algebra characteristic set method, the differential characteristic set method and the difference characteristic set method are introduced.The second chapter mainly introduces the concepts of difference equation and difference polynomial system characteristic set method, including the definition,lemma theorem, properties and algorithm of difference polynomial system.The third chapter introduces the application of solve the nonlinear difference equations by the difference characteristic set method. First in this chapter, we effect the difference equations which we study in the paper; secondly, we use the zero decomposition theorem and the related algorithms of difference characteristic set method to decompose the zero set of the effective difference equations into 35 group zero sets; at last we solve zero set in each group, and finally we get the solutions of the original difference equations.