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

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,, (z), Y~ (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 predetermined interval within any accuracy (subject to relative machine precision). It has been implemented and tested on different machines utilizing the above Bessel functions of various orders and several intervals of the argument.