高阶常系数非齐次线性微分方程的逆特征算子分解法  

The Method of Inverse Characteristic Operator Decomposition for the General Solution of High Order Non-homogeneous Linear Differential Equation with Constant Coefficients

作　　者：郑华盛[1] 

机构地区：[1]南昌航空大学数学与信息科学学院,江西南昌330063

出　　处：《大学数学》2014年第4期76-81,共6页College Mathematics

基　　金：江西省及南昌航空大学教学改革项目(JXJG-13-8-18;JY1329);江西省教育厅学位与研究生教育教学改革项目(JXYJG-2012-072);江西省及南昌航空大学研究生数值分析优质课程建设项目

摘　　要：提出一种求任意高阶常系数非齐次线性微分方程通解的逆特征算子分解新方法.其基本思想是:将逆特征算子按有理真分式的因式分解定理分解为一次因式逆算子的形式,使问题转化为求多个一阶常系数非齐次线性微分方程的通解.得到了二阶与三阶及两种特殊情况下更高阶常系数非齐次线性微分方程通解的一般公式.之后,通过实例验证了方法的可行性和有效性.A new method of inverse characteristic operator decomposition is presented for the general solution of arbitrary high order non-homogeneous linear differential equation with constant coefficients. The basic idea is as follows. Firstly, first-order inverse operator form is obtained to inverse characteristic operator by factorization theorem of rational proper fraction. And then it is converted into finding general solution of some first-order constant coefficients and non- homogenous linear differential equations. The general formulas of general solution are obtained to second-order and third- order and higher order non-homogenous linear differential equation with constant coefficients. Finally, an applicability and efficiency is verified by several examples.

关 键 词：常系数 非齐次 线性微分方程 逆特征算子 通解 

分 类 号：O175[理学—数学] O13[理学—基础数学]