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[Licence| Download | New Version Template] aeld_v1_0.tar.gz(48 Kbytes)
Manuscript Title: An improved algorithm and a Fortran 90 module for computing the conical function Pm-1/2+iτ(x)
Authors: Amparo Gil, Javier Segura, Nico M. Temme
Program title: Conical
Catalogue identifier: AELD_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 183(2012)794
Programming language: Fortran 90.
Computer: Any supporting a FORTRAN compiler.
Operating system: Any supporting a FORTRAN compiler.
RAM: A few MB
Keywords: Conical functions, Computational methods, Asymptotic expansions, Recurrence relations.
Classification: 4.7.

Nature of problem:
Conical functions appear in a large number of applications because these functions are the natural function basis for solving Dirichlet problems bounded by conical domains. Also, they are the Kernel of the Mehler-Fock transform.

Solution method:
The algorithm uses different methods of computation depending on the range of parameters: asymptotic expansions, quadrature methods and recurrence relations.

In order to avoid underflow/overflow problems, the admissible parameter ranges for computing the conical functions in standard IEEE double precision arithmetic are restricted to (x,m, τ) ∈ (-1, 1) × [0, 40] × [0, 100] and (x,m, τ) ∈ (1, 100) × [0, 100] × [0, 100].

Additional comments:
The module Conical uses a Fortran 90 version of the routine dkia (developed by the authors) for computing the modified Bessel functions Kia(x) and its derivative. This routine is included in the distribution file and is also available at http://toms.calgo.org.

Running time:
Depending on the parameter range: when numerical quadrature is used (for x < 0), the algorithm is 10 - 20 times slower than the computations made using asymptotic expansions + recurrence relations.