三区间复合型Riccati-Bessel方程边值问题的相似构造法

Similar Construction Method of Boundary Value Problem of Three-Interval Composite Riccati-Bessel Equation

针对三区间复合型Riccati-Bessel方程边值问题,通过对解式进行剖析和简化,发现该类边值问题的解具有连分数的形式且具有相似性,是由引解函数、相似核函数、内外边界和衔接条件系数组合而成。由此得到求解该类三区间复合型Riccati-Bessel方程边值问题的一种新方法——相似构造法。该方法极大地简化了求解过程,得到的解表达式简洁美观。

By analysing and simplifying the solution expressions of the three-interval composite Riccati-Bessel equation, it is found that the solutions of this type of boundary value problems are in the form of continuous fractions and similarity, which are combined by the induced solution function, similar kernel function, inner and outer boundaries, and articulation condition coefficients. Therefore, a new method to solve this type of three-interval composite Riccati-Bessel equation boundary value problems—“similarity construction method” is obtained. This method greatly simplifies the solution process, and the obtained solution expressions are simple and beautiful.