Legendre方程边值问题的解的相似结构  

The Similar Structure of Solution for the Boundary Value Problem of Legendre Equation

作　　者：夏文文[1] 李顺初[1] 桂东冬 

机构地区：[1]西华大学应用数学研究所,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：《嘉应学院学报》2015年第2期5-9,共5页Journal of Jiaying University

基　　金：四川省教育厅重点项目(12ZA164)

摘　　要：针对Legendre方程的边值问题,对其解式的相似构造进行了研究.发现其解式可以由相似核函数和左边界条件的系数构造,而相似核函数则可由引解函数和右边界条件构造,即其解式可以通过两个线性无关解和左右边界条件的系数构造.由此获得了求解该类问题的一种新方法——相似构造法.Based on the question of boundary value problem of composite Legendre system, this paper studied the similar structure of it solution expression. We found that its solution can be obtained by structuring similar kernel function with the coefficients of left boundary condition. While the similar kernel function is constructed by both the function of guide solution and the coefficients of right boundary condition. Namely, its solution can be obtained by structuring two liner independent solution of determining equation with the coefficients of left and right boundary condition. Hence, this paper put forward a new method of solving this class boundary value problem： the similar constructive method.

关 键 词：Legendre方程 边值问题 相似核函数 相似构造法 

分 类 号：O175[理学—数学]