复合Legendre方程边值问题解的相似结构法

The similar structure method for the solutionto the boundary value problem of the compound Legendre equation

为了研究复合型的Legendre方程边值问题,对复合Legendre方程边值问题的解式进行了探讨,探索发现可以通过构造相应的相似核函数并结合左边界条件中的系数,进而将复合Legendre方程边值问题的解式转化为一种具有特殊相似结构的形式,并且通过研究获得了一种方法,以此来求解该类边值问题——相似构造法.

In order to study the boundary value problem of the compound Legendre equation,the solution to the boundary value problem of the compound Legendre equation is put under examination.It is found that the corresponding similar kernel function can be constructed and in combination with the coefficients in the left boundary condition,the solution of the boundary value problem can then be transformed into a form with a special similar structure,and a method-the similar construction method-is obtained through research to solve this kind of boundary value problem.