求解一类Riccati-Bessel方程边值问题的新方法  

A New Method of Solving the Boundary Value Problem of a Class of Riccati-Bessel Equation

作　　者：王强[1] 李顺初[1] 蒲俊[1] 

机构地区：[1]西华大学应用数学研究所,四川成都610039

出　　处：《绵阳师范学院学报》2015年第5期1-7,11,共8页Journal of Mianyang Teachers＇ College

基　　金：四川省教育厅自然科学重点项目(12ZA164)

摘　　要：针对Riccati-Bessel方程一类边值问题进行求解,获得了解式的相似核函数和相似结构,通过进一步分析,发现求解该类边值问题可先利用Riccati-Bessel方程的两个线性无关解构造引解函数,再结合右边值条件的系数组装得到相似核函数;通过相似核函数和左边值条件的系数组装就可以得到Riccati-Bessel方程边值问题的解,由此提出了解决该类Riccati-Bessel方程边值问题的一种新思路——相似构造.This paper solved a boundary value problem of Riccati - Bessel equation;and the similar kernel function and similar structure of the solution were obtained. By further analysis and solving this class of boundary value problem,the guiding functions were firstly constructed by using two linearly independent solutions of Riccati- Bessel equation,and then the similar kernel function was assembled by the guiding functions and coefficient of right boundary value condition. The solution to the boundary value problem was assembled by similar kernel func-tion and coefficient of left boundary value condition. Therefore a new idea is put forward for solving this class of boundary value problem of Riccati - Bessel equation：similar structure.

关 键 词：边值问题 Riccati-Bessel方程 相似核函数 相似结构 引解函数 

分 类 号：O175[理学—数学]