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 approximation 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. Space Sci. 332:365, 2011), and (ii) for azimuth-angle dependent Fourier components, an already obtained solution of the next lower order term.
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Notes
Jablonski (2012) lately cast doubt on the numerical accuracy of the method developed by Kawabata and Limaye (2011): he erroneously states that the Kawabata–Limaye method yielded \(H(1,1)=2.9077901976\), while the more correct value is 2.9078105291. On the contrary, their method is capable of generating the values of \({}^{\mathrm{iso}}H(\varpi_{0},\mu)\) accurate at least to the 10th decimal figures for any combination of \(\varpi_{0}\) and \(\mu\) values as their Table 1 clearly shows. The value 2.9078105291 was mentioned in Kawabata and Limaye (2011) simply to warn the readers that such less accurate figures would result unless their method or something alike is employed.
A Fortran77 source program to calculate \(H\)-functions applying Method D is available from the author on request.
References
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The author is grateful to the anonymous referee for his or her constructive comments.
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Kawabata, K. A fast iterative method for Chandrasekhar’s \(\boldsymbol{H}\)-functions for general laws of scattering. Astrophys Space Sci 358, 32 (2015). https://doi.org/10.1007/s10509-015-2434-0
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DOI: https://doi.org/10.1007/s10509-015-2434-0