Airy方程的一类边值问题的解的相似构造法  

The similarity construction method of a kind of boundary-value problem of airy equation

作　　者：王芙蓉[1] 李顺初[1] 许东旭[1] 

机构地区：[1]西华大学应用数学研究所,四川成都610039

出　　处：《湖北师范学院学报（自然科学版）》2013年第1期79-85,共7页Journal of Hubei Normal University(Natural Science)

基　　金：国家科技重大专项项目(2008ZX50443-14);四川省教育厅自然科学重点项目(12ZA164);西华大学应用数学重点学科资助(ZXD0910-09-1)

摘　　要：针对Airy方程的一类边值问题,经变量替换将其转换成变型的Bessel方程的边值问题,通过研究解式的相似结构,得到了相似核函数;经分析,此边值问题可以先由Airy方程的任意两个线性无关的解和右边界条件系数构造出相似核函数,再由左边界条件中的系数决定的相似结构式进行组装,得到Airy方程的一类边值问题的解,从而获得求解该类边值问题的一个新方法——相似构造法;该方法对进一步的分析解的内在规律及编制相应的分析软件提供了新思路.Variable substitution are used in this paper to translate a kind of boundary-value problem of Airy equations into modified Bessel equations,and the similar kernel function is obtained through the analysis of the similar structure of solution.Solution of the equation boundary-value problem is acquired by structuring Similarity kernel function with any two linearly independence solutions of Airy equation and coefficients of right boundary condition first,and then assembling with the similar structure determined by the coefficients of left boundary condition,thus similarity construction method,a new method of solving this kind of boundary-value problem,is obtained;This method open a new way to analysis solution of the inherent law and design relevant analysis software.

关 键 词：Airy方程 边值问题 相似核函数 相似构造法 

分 类 号：O175[理学—数学]