三区复合型Tschebycheff方程边值问题的相似构造法  

Similar Construction Method of Boundary Value Problem of Three-Region Composite Tschebycheff Equation

作　　者：郑鹏社 杨雨 李顺初 桂钦民 ZHENG Pengshe;YANG Yu;LI Shunchu;GUI Qinmin(School of Science,Xihua University,Chengdu 610039,China;Beijing Dongrunke Petroleum Technology Co.,Ltd.,Beijing 100029,China)

机构地区：[1]西华大学理学院,四川成都610039 [2]北京东润科石油技术股份有限公司,北京100029

出　　处：《徐州工程学院学报（自然科学版）》2022年第4期8-14,共7页Journal of Xuzhou Institute of Technology(Natural Sciences Edition)

基　　金：西华大学研究生课程建设项目(YJSKC20204)。

摘　　要：在对三区复合型Tschebycheff方程的某类边值问题的探索中,主要研究了其内区、中区、外区解的结构,发现此边值问题解的表达式由Tschebycheff方程的两个线性无关解、内外边界条件和两组衔接性条件的系数组成,且此表达式的结构是类似于连分式的形式,因此提出并应用了求解此类边值问题的新办法——相似构造法.该方法能够降低求解的难度,提高计算结果的准确度.The structure of the solutions in the inner, middle and outer regions are mainly studied in the exploration of a kind of boundary value problem for the three-region composite Tschebycheff equation. It is found that the expression of the solutions of the boundary value problem is composed of two linear independent solutions of the Tschebycheff equation, the internal and external boundary conditions and the coefficients of two sets of convergence conditions.This structure of the expression is similar to the form of continued fractions. Therefore, a new method for solving this kind of boundary value problem-similar construction is proposed and applied in this paper. This method can reduce the difficulty of solving and improve the accuracy of calculation results.

关 键 词：Tschebycheff方程 边值问题 相似核函数 相似构造法 

分 类 号：O175.8[理学—数学]