Application Of Differential - Difference Feature Column Method In Accurately Solving Relativistic System

The development of science and technology makes the application ?eld of di?erential-di?erence equations get more widely. Although di?erence-di?erential equations are mainly used in various areas such as biology, economics, physics, control theory and technology. it is di?cult to solve the exact solutions of di?erentialdi?erence equations. In the past, Characteristic set method is applied to solve the algebraic equations. Recently, the Wu’s characteristic set method was expand to simply the di?erence systems and di?erential systems.In this thesis, based on the Wu’s characteristic set method of di?erentialdi?erence polynomial system proposed by Gao Xiaoshan and Luo Yong, we improves some algorithm in the di?erential-di?erence characteristic set method. The improvement is about the algorithm of solving the extension ?eld. With the improvement simply the relativistic Toda lattice system by the characteristic set method and obtained its exact solution by the direct method with maple.The thesis falls into three parts:The ?rst chapter introduces the development of mathematics mechanization,and the application in the algebraic systems, the di?erential systems and the di?erence of characteristic set method.In the second chapter we discussed the di?erential-di?erence characteristic set method and the improvement of this method. We improves the method by providing a new algorithm with a new de?nition. Then, we show the Wu’s zero decomposition algorithm.The third Chapter mainly gives the exact solution of relativity lattice Toda equations by using the characteristics of algorithm, and the solution of equations can be decomposed into several zero sets. Finally, the system was solved by the direct method. Exact solution of relativity lattice Toda equations is obtained.