DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION

Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (8): 880-887.

DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION

柯红路¹, 谢和熙²

1. Applied Pansystems Institute, Chongqing University of Architecture and Engineering, Chongqing 400045, P R China;
2. Chongqing Jiaotong Institute, Chongqing 400074, P R China

收稿日期:1998-04-02 修回日期:1999-01-25 出版日期:1999-08-18 发布日期:1999-08-18

DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION

Ke Honglu¹, Xie Hexi²

1. Applied Pansystems Institute, Chongqing University of Architecture and Engineering, Chongqing 400045, P R China;
2. Chongqing Jiaotong Institute, Chongqing 400074, P R China

Received:1998-04-02 Revised:1999-01-25 Online:1999-08-18 Published:1999-08-18

摘要/Abstract

摘要： In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge.

关键词: linear ordinary differential equation, differentiator series method, special solution, general solution

Abstract: In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge.

Key words: linear ordinary differential equation, differentiator series method, special solution, general solution

中图分类号:

O175.3

柯红路;谢和熙. DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(8): 880-887.

Ke Honglu;Xie Hexi. DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(8): 880-887.

参考文献

[1] Lustealnic L A,Sobolef B E.Outline of Functional Analysis[M].Translated by Yang Congren.Beijing:Science Press,1964,102~110.(Chinese vision).
[2] Ke Honglu.Differentiator series method and its application in differential equation[J].Journal of Yuzhou University,1998,15(3):11~16.(in Chinese).
[3] Ke Honglu.Dif erentiator Series Method and to Solve Linear Differential Equation with Constant Coefficient[M].Chongqing:Press of Department of Natural Science,Chongqing University of Architecture and Engineering,1996.(in Chinese).
[4] Zeng Shuliang.One method of special solution for linear differential equation of second order[J].Journal of Neijiang Education College,1996,(2):63~67.(in Chinese)
[5] Ke Honglu,Tang Yuqi.A special solution to one class non_homo geneo us differential equation by the differential operator series method[J].Journal of Logistica l Engineering University,1995,11(4):56~60.(in Chinese).
[6] Ke Honglu.Operator solution for one class of Cauchy problem[J].Journal of Chongqing University of Architecture and Engineering,1989,11(3):30~36.(in Chinese).
[7] Ke Honglu.Calculation of generalized integrals using differentiator series method[J].Journal of Chongqing University of Architectur e and Engineering,1996,18(1):110~ 113.(in Chinese).
[8] Ke Honglu.Calculation of generalized integrals using differentiator series method[J].Journal of Chongqing University of Architectur e and Engineering,1996,18(1):110~113.(in Chinese).
[9] Ke Honglu.One new calculation of number characteristics of randam vector function[J].Engineering Mathematics,1997,13(1):155~159.(in Chinese).
[10] Xie Huox i,Ke Honglu.Solution of differential operator series in two sorts of problem and its application[J].Journal of Chongqing College of Teachers,1997,14(1):41~45.(in Chinese).

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DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION

DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION

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