几类常系数非齐次线性差分方程解的研究

The research for the solutions of several types of linear difference equations with constant coefficients

文章讨论了几类k阶常系数非齐次线性差分方程,并根据非线性项的特征,利用算子方法及其相关引理将其化为更高阶齐次线性差分方程.通过相应高阶齐次线性差分方程的通解形式,获得其特解的简单表达形式,从而获得非齐次线性差分方程通解形式.

In this paper, we discuss several types of k-order non-homogeneous linear difference equations with constant coefficients. According to the character of the equations, we transfer them to higher order homogeneous linear difference equations by the operator method and some lemmas. By the representation of general solutions of the higher order homogeneous linear difference equations, we obtain a special solution of the original nonhomogeneous linear difference equation, and then the general solutions of the non-homogeneous linear difference equation are obtained.