由任一非零特解构造复合微分方程边值问题的解

针对二阶线性齐次微分方程边值问题,本文研究了解式的相似结构,获得了相似核函数;说明了该类微分方程边值问题的解,可以首先由定解方程的任一非零特解和某一边界条件的系数构造出相似核函数,再由另一边界条件中的系数决定的相似结构式进行组装,即可得到二阶线性齐次微分方程边值问题的解;这种不必去具体繁琐地进行推导求解的方法就是所谓的相似结构构造法(简称相似构造法),该法是解决微分方程的复杂边值问题和解决有关工程科学问题的一个创新的思想和简单而行之有效的方法.

Constructing the solution of boundary value problem of the differential equation with it's a arbitrary non-trivial solution

Based on the analysis of the solutions for a boundary value problem of the second order linear homogeneous differential equation, this paper studied the similar structure and the similar kernel functions of the solutions and put forward a new method of solving this class boundary value problem: the similar constructive method. As a matter of fact, the similar kernel function be constructed by the arbitrary non trivial solution of definite equation and the coefficient of right boundary condition firstly, the similar structure formula is determined by left boundary condition secondly, and then the particular solution can be obtained. Consequently, this method are an innovative idea and a simple effective method of solving the boundary value problem of the differential equation and when used in practical engineering science also.