Solving A Class Of Biological Model Equation By Using The Difference Characteristic Column Method

The Wu’s characteristic set method is the central algorithm of the theory of mathematic mechanization. At present, it has been used in the mechanical theory for proving, solving algebraic equations, numerical control and other ?elds. In recent years, theories and algorithms of the characteristic set methods of di?erential, di?erence and di?erential-di?erence equations have been given and gradually revived.In this paper, the di?erence characteristic set method is used to study the zero set of a class of nonlinear di?erence equations of biological properties. First of all, we make some improvements on the algorithm of irreducible decomposition,making pseudo remainder into several orders lower due to type, thereby reducing the amount of computation. Then we study the zero decomposition theorem and decompose zero set of the di?erence equations into the union of the several zero sets.The zero sets corresponds to the appropriate characteristic sets of triangular form.By solving there characteristic sets, we can get the solutions of the equations. The order of characteristic sets of triangular form are lower than the order of the original equations and was easier to solve. Finally, making use of symbolic computation software Maple and Z transformation, we get the exact solutions of the equations.This paper is divided into three parts as follow: the ?rst chapter brie?y describes the background of di?erence equations; the second chapter is preliminary knowledge; the third chapter is the central of this paper, namely solving di?erence equations.