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Manuscript Title: The Chandrasekhar function revisited
Authors: A. Jablonski
Program title: CHANDRAS_MIX
Catalogue identifier: AEWW_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 196(2015)416
Programming language: FORTRAN 90.
Computer: Any.
Operating system: Windows XP, Windows 7, Windows 8, Linux.
RAM: 1.0 Mb
Keywords: Chandrasekhar function, Isotropic scattering, New solutions, New optimized code, High accuracy tabulation, Particle transport in condensed matter.
Classification: 2.4, 7.2.

Nature of problem:
Algorithms derived from an integral representation of the H function generally exhibit a slow convergence which may considerably delay calculations involving integration of functions containing the H function. Furthermore, a set of reference values of the H function of a very high accuracy is useful in analysis of performance of different algorithms, and thus a relevant computational procedure is needed for that purpose.

Solution method:
Problem of slow convergence is circumvented by the derivation and use of an analytical solution sufficiently accurate in the range of small arguments. In the range of arguments exceeding 0.05, a new integral representation is derived that is rapidly converging and can be easily adjusted to calculations with accuracy of 21 significant digits. A mixed algorithm is constructed that is optimized with respect to the execution time.

The arguments for the Chandrasekhar function, x and omega (notation used in the code), are restricted to the range: 0<=x<=1 and 0<=omega<=1.

Unusual features:
The Gauss-Legendre quadrature is used in calculations of the H function from different integral representations. The optimum number of abscissas, N, was found to be equal to 20. To control accuracy, the bipartition approach is used, i.e., calculations are repeated after halving the integration interval until the desired accuracy is reached.

Running time:
On average, about 11 microseconds for both arguments of the Chandrasekhar function exceeding 0.05.