一类二阶齐次线性差分方程的通解及其应用

来源期刊：中南大学学报(自然科学版)2002年第2期

论文作者：周英告

文章页码：218 - 220

关键词：齐次线性差分方程;对称型差分方程;通解;数学模型

Key words：homogeneous linear difference equation; symmetric difference equation; general solution; math ematica model

摘    要：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,从而为求解结构力学等问题提供了便利.

Abstract: We knowthe 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,…, butwe cannot get the general solution of the difference equation generally. In this paper, the author discusses the general solution of second-order homogeneous linear different equations on condition that there exists a solution, thus, we use some techniques to obtain the general solution of those special difference equations.