一类二阶齐次线性差分方程的通解及其应用

General solution of second-order homogeneous linear difference equations and its application

对一般形式的二阶齐次线性差分方程y(n +2 ) +p(n)y(n +1) +q(n)y(n) =0和y(n +2 ) +p(n)y(n +1)+y(n) =0 ,已用于求解结构力学、动态经济学问题以及数学建模等 .但人们通常只知道这类方程解的结构 ,难以直接求出其显式解 .作者在假设已经获得一个特解的前提下 ,找出了这类差分方程的通解公式 ;此外 ,获得了一类特殊形式差分方程的更为直接的解和一些推论 。

We know the structure of solution on second order homogeneous linear difference equations such as y(n+2)+ p(n)y(n+1)+q(n)y(n)=0, n =0,1,2,..., but we cannot get the general solution of the difference equations generally. In this paper, the author discusses the general solution of second order homogeneous linear difference equations on condition that there exists a solution, thus, we use some techniques to obtain the general solution of those special difference equations.