Bessel函数近似解法比较

Comparisons of approximate solving methods for the Bessel functions

利用差分方法求Bessel方程的数值解;并与Bessel函数的2种级数表达式的计算结果进行比较,通过数值计算及相应的分析得出,Bessel方程的数值解与级数解各有利弊;利用计算机,由差分方法计算,无需考虑自变量的大小,但其解是离散的,不可进行解析运算;而由2种级数表达式计算时,必须关注自变量的大小,但可以利用它们进行解析运算。

Using the difference method, the numerical solutions of Bessel equations are given. The computing results of this method and two series expansions of Bessel functions are compared. The computing results and analysis show advantages and disadvantages of the numerical and series solutions of Bessel equations. The functional values can be computed by the difference method without considering the values of free variables, but the solutions are discrete and cannot be used in analytic operations; while in computation using two series expansions, the values of free variables must be considered, and the two series expansions can be used in analytic operations.