Abstract
The purpose of this paper is to present a numerical technique to directly compute the Chandrasekhar'sH (μ)-function for anisotropic scattering in terms of the roots of the characteristic equations as well as the quadrature points of a certain degreen employed to approximate the definite integral involved in the basic equation. The principal feature of the algorithm proposed here is a compact computer code to enumerate n C m combinations ofn distinct integers {1,...,n} takenm at a time. With these quantities available, the coefficients of the polynomial equation of the characteristics equation can be readily computed for any given characteristic function, so that a standard technique such as the Laguerre method can be applied to find all the roots.
It is shown that the results obtained for some representativeH(μ)-functions using the present technique with relatively low-order formula (e.g.,n=7) are sufficiently accurate for all practical purposes.
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Kawabata, K., Satoh, T. & Ueno, S. A direct numerical approach to the Chandrasekhar'sH-functions for arbitrary characteristic functions. Astrophys Space Sci 182, 249–260 (1991). https://doi.org/10.1007/BF00645005
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DOI: https://doi.org/10.1007/BF00645005