运用差分特征列方法精确求解一类非线性有理差分方程  

Using differential characteristic set method to accurately solve a class of nonlinear rational difference equations

作　　者：程欣宇 蒋鲲[1] CHENG Xinyu;JIANG Kun(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2024年第3期264-271,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(31570492)。

摘　　要：运用差分特征列方法来求解一组有理差分方程,即一类非线性差分方程。首先介绍了差分方程及特征列方法的理论知识,进而运用差分特征列方法对一类非线性差分方程组进行化简,通过有效化、判断一致性、可约分解等步骤,最终根据整序定理和零点分解定理得到这类非线性零点集。The differential characteristic set method has been used to solve a set of rational difference equations,namely a class of non-linear difference equations.The theoretical knowledge of difference equations and characteristic set methods is introduced firstly.Then,the difference characteristic set method is applied to simplify a class of nonlinear difference equation systems.Through steps such as effectiveness,consistency judgment and reducible decomposition,the zero point set based on the whole order theorem and zero decomposition theorem is finally obtained.

关 键 词：差分方程 特征列方法 非线性 零点集 

分 类 号：O175[理学—数学]