一类二阶微分方程边值问题解的相似结构

Similar Structure of Solutions to a Class of Second-Order Differential Equation Boundary Value Problems

通过分析一类二阶微分方程边值问题解的表达式,发现此边值问题的解的表达式都呈现连分式乘积形式,是由六个引解函数组成的相似核函数和左边界条件系数构造而成。由此得到求解该类边值问题的相似结构解的相似构造法,并对一个具体的二阶微分方程边值问题进行求解。该方法降低了求解难度,得到的解表达式简洁明了,更能清晰地反映各个参数对解的影响。

By analysing the expressions of the solutions of a class of second-order differential equation boundary value problems, it is found that the expressions of the solutions of this boundary value problem are all in the form of a continuous fractional product, which is constructed by the similar kernel function consisting of six induced solution functions and the left boundary condition coefficients. As a result, the similar construction method for solving similarly structured solutions of this class of boundary value problem is obtained, and a specific second-order differential equation boundary value problem is solved. The method reduces the difficulty of the solution, and the obtained solution expression is concise and more clearly reflects the influence of each parameter on the solution.