一类常系数线性差分方程的特解探究

针对一类常系数线性差分方程，运用特征函数法和比较系数法，得到了方程特解的显式表达．当方程非齐次项μ^kPm（k）中多项式Pm（k）=A（A为非零常数）时，可采用特征函数法得到方程的一个公式化特解；当Pm（k）=dmk^m＋dm-1k^m-1＋…＋d0（d0≠0）时，可采用比较系数法来得到方程的一个特解．该方法简单易行，特解形式直观，避免了以前方法计算量过大的不足．

Research on the Special Solution of a Kind of Linear Difference Equation with Constant Coefficient

In this article, we use methods of characteristic function and comparing coefficient to deduce the expression of the special solution of a kind of linear difference equation with constant coefficient. When polynomial Pm （k） = A（A is non-zero constant ） in the non-homogeneous item μ^kPm（k） , method of characteristic function is used ; When Pm（k） = dmk^m ＋dm-1k^m-1 ＋ … ＋d0（dm≠0） ,we can deduce the formula of the special solution of the equation from method of comparing coefficient. The two methods avoiding the defect of some old methods which calculate excessively are simple and doable, and the special solution has an intuitionistic expression.