RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions

Abstract
A portable software package, named RFSFNS, is presented for the localization and computation of the simple real zeros of the Bessel functions of first and second kind, J_v (z), Y_v (z), respectively, and their derivatives, where v ≥ 0 and z > 0. This package implements the topological degree theory for the localization portion and a modified bisection method for the computation one. It localizes, isolates and computes with certainty all the desired zeros of the above functions in a predetermi...

Title of program: RFSFNS
Catalogue Id: ADCK_v1_0

Nature of problem
Bessel functions and their zeros are encountered in many problems of Mathematical Physics, such as: the cyclic membrane vibrations, the temperature distribution in a solid cylinder or in a solid sphere, the diffraction of a plane electromagnetic wave by a conducting cylinder, the quantum billiards, etc.

Versions of this program held in the CPC repository in Mendeley Data
ADCK_v1_0; RFSFNS; 10.1016/0010-4655(95)00115-9

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
本文提出一款名为RFSFNS的可移植软件包，用于定位并计算第一类贝塞尔函数（Bessel functions of the first kind）$J_v(z)$、第二类贝塞尔函数（Bessel functions of the second kind）$Y_v(z)$及其导函数的单实零点，其中参数$vgeq0$且$z>0$。该软件包的定位模块采用拓扑度理论（topological degree theory）实现，计算模块则采用改进型二分法（modified bisection method），可确定性地对上述函数在预设范围内的全部目标零点完成定位、隔离与数值求解。

程序名称：RFSFNS
目录编号：ADCK_v1_0

问题属性
贝塞尔函数（Bessel functions）及其零点广泛出现于诸多数学物理问题中，例如：循环膜振动、实心圆柱或实心球体的温度分布、导电圆柱对平面电磁波的衍射、量子台球（quantum billiards）等。

Mendeley数据中的CPC程序库（CPC Program Library）收录的本程序版本
ADCK_v1_0; RFSFNS; 10.1016/0010-4655(95)00115-9

本程序源自贝尔法斯特女王大学所维护的CPC程序库（1969-2019）