三区间复合Laguerre方程边值问题的解的相似结构

Similar structure of solution of the boundary value problem of three-region composite Laguerre equation

对一类三区间复合Laguerre方程边值问题的解式进行研究,发现其解的结构具有相似性。其解式可以通过定解条件的系数、引解函数及相似核函数组装而成。其中引解函数通过定解方程的两个线性无关解构造而成,相似核函数由定解条件的系数和引解函数构造而成,从而提出了应用相似构造法来解决三区间复合Laguerre方程的边值问题。

For a class of three-region composite Laguerre equation boundary value problems,we have analyzed its solutions and found that the structures of its solutions are similar.We have found that its solution can be assembled from the coefficients of the definite solution conditions,the function of guide solution and the similar kernel function,where the function of guide solution is constructed from two linearly independent solutions of the definite solution equation and similar kernel functions are constructed from the coefficients of the definite solution conditions and the function of guide solution.Therefore,we propose a new method to solve this kind of boundary value problem,which is named similarity construction method.