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[Licence| Download | New Version Template] aeld_v1_0.tar.gz(48 Kbytes) | ||
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Manuscript Title: An improved algorithm and a Fortran 90 module for computing the conical function P^{m}_{-1/2+iτ}(x) | ||

Authors: Amparo Gil, Javier Segura, Nico M. Temme | ||

Program title: Conical | ||

Catalogue identifier: AELD_v1_0Distribution 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. | ||

Restrictions: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 K and its derivative. This routine is included in the distribution file and is also available at http://toms.calgo.org._{ia}(x) | ||

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. |

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