A direct numerical approach to the Chandrasekhar's H-functions for arbitrary characteristic functions

Details A direct numerical approach to the Chandrasekhar's H-functions for arbitrary characteristic functions A direct numerical approach to the Chandrasekhar's H-functions for arbitrary characteristic functions

Aug 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991ap%26ss.182..249k&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 182, no. 2, Aug. 1991, p. 249-260.

Astronomy and Astrophysics

Astrophysics

2

Chandrasekhar Equation, Eigenvalues, Eigenvectors, Radiation Distribution, Scattering Functions, Computer Programs, Iterative Solution, Laguerre Functions

Scientific paper

The purpose of this paper is to present a numerical technique to directly compute the Chandrasekhar's H(mu)-function for anisotropic scattering in terms of the roots of the characteristic equation as well as the quadrature points of a certain degree n employed to approximate the definite integral involved in the basic equation. The principal feature of the proposed algorithm is a compact computer code to enumerate nCm combinations of n distinct integers (l,...,n) taken m at a time. With these quantities available, the coefficients of the polynomial equation of the characteristic 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 representative H(mu)-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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