# ELF and GNOME: Two tiny codes to evaluate the real zeros of the Bessel functions of the first kind for real orders

## Description

Abstract Two codes to evaluate the real zeros (j_(v,s)) of the Bessel functions of the first kind J_v (x) for real orders v are presented. The codes are based on a Newton-Raphson iteration over the monotonic function f_v (x) = x^(2v-1)J_v (x)/J_(v-x)(x). The code ELF is a remarkably short program for finding, given any starting value x_0 >0 and any real order, the zero of J_v (x) in the neighborhood of x_0(x_0and the zero in the same branch of f_v (x)). GNOME is a modification of ELF for fi... Title of program: ELF, GNOME Catalogue Id: ADJY_v1_0 Nature of problem We include two codes in order to evaluate the zeros of first kind Bessel functions for real orders nu: The subroutine ELF finds the zero jnu,s of the first kind Bessel function Jnu(x) in the neighbourhood of a given starting value x0 (x0 and jnu,s in the same branch of Hnu(x)=Jnu(x)/Jnu-1(x)). The subroutine GNOME finds the zeros in a given interval [xmin, xmax]. The zeros of first kind Bessel functions appear in the solution of many different physical and engineering applications: wave guides, ... Versions of this program held in the CPC repository in Mendeley Data ADJY_v1_0; ELF, GNOME; 10.1016/S0010-4655(98)00193-3 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)