A Fast Iterative Method for Chandrasekhar's H-functions for General Laws of Scattering

TL;DR

This paper introduces an accelerated iterative method for computing Chandrasekhar's H-functions for general scattering laws by using improved initial approximations, significantly speeding up calculations in astrophysics applications.

Contribution

The authors propose a novel initialization approach for iterative H-function calculations, combining simple formulas for isotropic cases and lower-order solutions for azimuth-dependent cases, enhancing computational efficiency.

Findings

Accelerated convergence of H-function calculations achieved.

Effective initial approximations reduce iteration count.

Method applicable to general scattering laws in astrophysics.

Abstract

This work shows that notable acceleration of the speed of calculating Chandrasekhar's H-functions for general laws of scattering with an iterative method can be realized by supplying a starting pproximation produced by the following procedure: (i) in the cases of azimuth-angle independent Fourier components, values of the isotropic scattering H-function given by an accurate yet simple-to-apply formula, in particular, the one by Kawabata and Limaye (Astrophys. and Space Sci. Vol. 332, 365-371, 2011 DOI 10.1007/s10509-010-0512-x; see also Astrophys. and Space Sci. Vol. 348, 601, 2013 DOI 10.1007/1009-013-1589-9, for erratum), and (ii) for azimuth-angle dependent Fourier components, an already obtained solution of the next lower order term. The paper has been published in Astrophys. and Space Sci. Vol. 358, 32-38 (2015) DOI 10.1007/s10509-015-2434-0, and the final publication is available at link.springer.com.