摘要
通过对二阶齐次线性微分方程边值问题的解析表达式进行整理和简化,得到了解式的相似结构形式;说明了该类微分方程的解,具有类似于实数可表为连分式,图形具有相似性的所谓式相似性质;指出了解式的相似性质的研究,有利于进一步地分析解的内在规律,解决相应的应用问题,方便编写相应的分析软件;它是微分方程理论的新发展。
The solution＇ s formal similarity is gained by reducing the analytical expression of boundary value problems for a class of second-order linear homogeneous differential equations. It is can be seen from this similar structure that the class equation will be obtained by the product of several fractions and the graphs have similarity as well. The character of the structure resembles that of real number. The result attained in this paper benefits the understanding of the inherent laws of relevant engineering sciences and the design of practical analysis software. Furthermore, it promotes the development of the equation theory.
出处
《西华大学学报（自然科学版）》
CAS
2009年第5期40-41,90,共3页
Journal of Xihua University:Natural Science Edition
关键词
常微分方程
二阶齐次线性方程
边值问题
解式
相似结构
式相似
ordinary differential equation
second-order linear homogeneous equation
boundary value problem
solution ＇ s formula
similar structure
formal similarity
作者简介
李顺初（1963-），男，湖北浠水人，教授，主要研究方向为应用数学、微分方程。
