三阶线性变系数差分方程的Mikusiski算符解法(Ⅲ)*
Mikusiński’s Operators Solution of Three-Order Linear Difference Equation with Variable Coefficients
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摘要: 本文在[3],[4]工作的基础上,利用变数算符的思想以及Mikusiński算符域中移动算符和变系数移动算符级数的有关结果,解决了一般的三阶线性变系数差分方程的求解问题,并且绘出了一些特殊的三阶线性变系数差分方程的更好的解式;此外,还试图为实现更高阶线性变系数差分方程的求解提供思想方法。
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关键词:
- Mikusiński算符 /
- 移动算符 /
- 差分方程
Abstract: This paper proceeds the papers [3] [4],we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators series with variable coefficients in the operational field of Mikusinski,it is devoted to the solution of the general three-order linear difference equation with variable,coefficients,and it is also devoted to the better solution .formula for the some special three-order linear difference equations with variable coefficients,in addition,we try to provide the idea and method for realizing solution of the more than three-order linear difference equation with variable coefficients.-
Key words:
- Mikusinski operator /
- shift operator /
- difference equation
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[1] Mikusinki,J.,Operational Calculus,Pergamon Press,New York (1959). [2] Qiu Lian-rong,A direct method of operatid}.al calculus (I),Acta Mathematica Scientia,(1982),389-402. [3] 周之虎,差分方程的Mikusiński算符解法(I)(待发表). [4] Zhi-hu,Mikusinski operator's sblution of difference equation (II)-The solution of the second-order linear difference equation with variable coefficients. [5] 周之虎,关于“算符演算”中的移动算符级数的一点注记,数学的实践与认识,(4) (1990),90-92. [6] 邱廉荣,直接算符演算法的新进展—关于n阶变系数线性常微分方程的解法,西北工业大学学报.5 (4)(1987),417-426. -
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