NonLTE transfer  IV. A rapidly convergent iterative method for the WienerHopf integral equations.
Abstract
It is shown that a simple approximation previously derived for the source function in the isothermal case of nonLTE line transfer with complete frequency redistribution can be extended into a rapidly convergent iterative scheme for solving WienerHopf integral equations. The convergence of the method and its numerization are discussed, and the iterative scheme is used for the singular integral equation of the interior asymptotic expansion as well as the homogeneous WienerHopf equation for the boundary layer. Analogs for these equations based on the approximation for the source function are presented. Consideration is given to the extent to which the leading terms of the asymptotic expansions arising when epsilon tends to zero may be employed in practice to determine the source function for finite epsilon.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 November 1977
 DOI:
 10.1093/mnras/181.2.281
 Bibcode:
 1977MNRAS.181..281F
 Keywords:

 Iterative Solution;
 Radiative Transfer;
 Thermodynamic Equilibrium;
 Wiener Hopf Equations;
 Astrophysics;
 Asymptotic Series;
 Convergence;
 Series Expansion;
 Astrophysics