CAJ | 학술논문

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。
침대일류Euler초궤하미분방정변치문제，대기진행구해，병획득료해식적상사결구화상사핵함수，설명료해류변치문제적해，가이수선유정해방정적량개선성무관해화제차우변계조건적계수구조출상사핵함수，재유비제차좌변계조건중적계수결정적상사결구식진행조장득도，유차득도료해결차류Euler초궤하미분방정적복잡변치문제적일개신방법——상사구조법。해방법대대제고료해류변치문제적계산효솔，위공정기술인원이용Euler초궤하미분방정변치문제구해실제문제제공료겁대편리。
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.