Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

[Licence| Download | New Version Template] aczp_v1_0.gz(19 Kbytes)
Manuscript Title: Bessel functions Jnu(x) and Ynu(x) of real order and real argument.
Authors: J.B. Campbell
Program title: BESSJY
Catalogue identifier: ACZP_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 18(1979)133
Programming language: Fortran.
Computer: IBM 3032.
Operating system: TSS/370.
RAM: 12K words
Word size: 32
Keywords: General purpose, Bessel, Axisymmetric, Asymptotic expansion, Backward recurrence, Continued fraction.
Classification: 4.7.

Nature of problem:
The BESSJY package calculates Bessel functions Jnu(x) and Ynu(x) of real order and real argument. These functions are used for the solution of potential problems in cylindrical coordinates.

Solution method:
For extremely small argument, Jv(x) and Yv(x) are determined from their limiting forms for small arguments. For small or moderately large argument, Jv(x) is calculated by Miller's backward recurrence algorithm described by Gautschi, Yv(x) and Yv+1(x) for |v| <= 1/2 are determined from Neumann series of functions Jv+2m(x) as described by Goldstein and Thaler, and Yv+k(x) for k >= 2 is determined from the forward recurrence formulae. For large argument, the Bessel functions are determined from the asymptotic expansions for large argument and the recurrence relations.

Restrictions:
The functions are determined only for non-negative order. Jv(x) is determined only for non-negative argument and Yv(x) is determined only for positive argument. The subroutines are inefficient when both order and argument are very large.

Running time:
For argument and order not both very large, the determination of a single function requires less than 1 ms. The determination of a single function requires less than 1 ms. The determination of a sequence of functions requires, in addition, approximately 10 mu s for each member of the sequence. Some typical CPU times are given in section 5 of the Long write-up.