求解第一种Weber方程边值问题的相似构造法

Similar Structured Method of Solution to Boundary Value of First Weber Equation

针对第一种Weber方程的边值问题,该文对其解式的相似构造进行了研究,并获得了相似核函数。由此得出如下结论:该边值问题的解首先可以由定解方程的两个线性无关解和右边界条件中的系数来构造相似核函数,再由左边界条件中的系数所确定的相似结构式进行组装而得到。最终获得了求解该类边值问题的新方法 -相似构造法,它既是一种解决复杂边值问题的代数方法,也是一种数学创新思维。

Aiming at the boundary value problem of the first Weber Equation, this paper does a research on the similar structure of it＇s solution expression, and the similarity kernel function is acquired. Thus, conclusions are made as follows ： Firstly, solution of the equation boundary value problem is acquired by structuring similarity kernel function with the two linear independence solutions of determining equation and coefficients in the right boundary conditions. Secondly, the solution is assembled with similar structure which is determined by the coefficients in the left boundary conditions. Finally, similar structured method, a new method of solving such boundary value problem is acquired. It is not only a no - logo theory and method, but also a kind of mathematics creative thinking.