线性变系数差分方程的时域求解方法

A Study on the Solutions of Time Domains of Linear Difference Equations With Variable Coefficients

以线性变系数微分方程的求解方法为依据,用类比法,提出了序列的原序列的概念,提出了后向差分运算对应的逆运算,即序列的不定求和,揭示了线性变系数差分方程的解结构。导出了一阶线性变系数差分方程的通解公式,基于一阶线性变系数差分方程的通解公式,利用降阶方法,导出了二阶线性变系数差分方程的通解公式,有效地解决了部分线性变系数差分方程的时域求解问题。

Based on the solutions of linear differential equations with variable coefficients,by means of the method of analogy,this paper introduces the concept of original sequences of sequences as well as inverse operations corresponding with backward difference operations,that is,indefinite summations of sequences,which reveal the structures of solutions of linear difference equations with variable coefficients.In addition,the general solution formulas for first-order linear difference equations with variable coefficients can be derived.Based on the formulas,depending on the method of the reduction of order,the general solution formulas for second-order ones can be derived as well,which are effective in the solutions of time domains of some linear difference equations with variable coefficients.