Wu Characteristic Set Exact Solution Of A Class Of Differential Equations For Research

In recent years, the discrete systems are widely using in economics, physics andengineering technology, and the discrete variable diferential system is described toget the attention of scholars, which became a hot issue of Computational Mathemat-ics, Applied Mathematics and Systems Science. Although the numbers of scholarshave conducted a large and detailed study of the existence and stability of solutionof the diferential system, there is no specific algorithm for the practical applicationof solving the exact solution of diferential equations.In this paper, the diference characteristic set method which is proposed byGaoxiaoshan, Luoyong.etc. It is used to solve nonlinear diferential polynomialgroup by this method. Using the algebraic point of view to examine the zero setsof diferential polynomial equations, the consistent irreducible characteristic set ofthe diferential polynomial is obtained in using of diference pseudo-remainders, dif-ference ascending chains, zero decomposition theorem theory and algorithms. Thezero decomposition of the diferential equations is provided to be a union of irre-ducible saturation ideal zero, and the exact solution of this second-order nonlineardiferential equations is obtained.The paper is organized as follows:The first chapter introduces the subject of background. a brief course of devel-opment of the characteristic set method is provided, the content and developmentdirection of the Wu characteristic set of polynomial systems is explained from threeaspects of algebra, diferential and diference, and the main content and researchvalue in this paper.Chapter II the basic theory. This chapter will be involved in some of the theoret-ical knowledge such as: diferential equations, Wu characteristic set of polynomialdiferential system. The theoretical support is provided for the follow-up to thepractical application. Given in Chapter III the several important algorithms and constraints combinedwith the previous theoretical basis of the diferential system Wu characteristic set.The Wu characteristic set of the diferential system is actually used to solve thesecond-order nonlinear diferential equations and their exact solution.