Euler超几何微分方程边值问题解的相似构造法

Similar Constructive Method of Solution for the Boundary Value Problem of Euler Hyper-geometric Differential Equation

针对一类Euler超几何微分方程边值问题,对其进行求解,并获得了解式的相似结构和相似核函数,说明了该类边值问题的解,可以首先由定解方程的两个线性无关解和齐次右边界条件的系数构造出相似核函数,再由非齐次左边界条件中的系数决定的相似结构式进行组装得到,由此得到了解决此类Euler超几何微分方程的复杂边值问题的一个新方法———相似构造法。该方法大大提高了该类边值问题的计算效率,为工程技术人员利用Euler超几何微分方程边值问题求解实际问题提供了极大便利。

A type of boundary value problem of Euler hyper-geometrie differential equation was solved in this paper. The similar structure of solution and the similar kernel function are gained consequently. The paper illustrates that the solution of this class of boundary value problem can be obtained as follows ： First- ly, constructing the similar kernel function as two independent solutions of the boundary value problem＇ s fixed equation on the singular point of zero is taken and the coefficients of the homogeneous right boundary condition in the boundary value problem; Furtherly, package the similar kernel function and the similar structure formed as the coefficients of the inhomogeneous left boundary condition in the boundary value problem; And then the solution can be gained. A new method-similar constructive method which is used to solve the complex boundary value problem of Euler＇ hyper-geometric differential equation is proposed as a result. This method improves the operation efficiency greatly and provides much convenience for engi- neers when they use boundary value problem of Euler hyper-geometric differential equation to solve practi- cal problems.