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Manuscript Title: RFSFNS: a portable package for the numerical determination of the number and the calculation of roots of Bessel functions. See erratum Comp. Phys. Commun. 117(1999)290.
Authors: M.N. Vrahatis, O. Ragos, T. Skiniotis, F.A. Zafiropoulos, T.N. Grapsa
Program title: RFSFNS
Catalogue identifier: ADCK_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 92(1995)252
Programming language: Fortran.
Computer: HP-715 (+PA-Risc 7100).
Operating system: UNIX, MS-DOS.
RAM: 60K words
Word size: 32
Keywords: Bessel functions, Simple real zeros, Topological degree, Kronecker-picard, Integral, Localization of zeros, Isolation of zeros, Bounds of zeros, Bisection method, Computation of zeros, Steed's method, Barnett's algorithm, General purpose.
Classification: 4.7.

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.

Solution method:
The total number of real zeros of a Bessel function is obtained using Picard's extension and Kronecker integral representation of the topological degree. Subsequently, a modified bisection method is employed for the computation of these zeros.

The functions considered here are Bessel functions of first and second kind and their first derivatives. Their order is real and non negative while their argument has to be positive.

Running time:
On an HP-715 computer (with a PA-Risc 7100/75 MHz processor) using the HP FORTRAN/9000 compiler, the elapsed CPU times for the computation of the total number of zeros in the given interval, their isolation and their computation, for the four test runs of Section 4, were as follows: (1) 9.02, 0.64, 29.56 msec, (2) 11.53, 0.75, 39.58 msec, (3) 14.27, 0.89, 46.87 msec and (4) 32.81, 1.91, 94.33 msec. The corresponding times on a PC IBM compatible (with an i486/66 MHz processor) using Microsoft Fortran 5.10 were on average 0.20, 0.05, 0.60 sec.