Iterative Solution for the Source Function in the Grey Atmosphere in Radiative Equilibrium.
Abstract
An iterative solution for the source function in the grey atmosphere in radiative equilibrium, first derived by Uns6ld [A. Uns6ld, Physik Der Sternatmospha~ren (SpringerVerlag, Berlin, 1955), p. 142~, is rederived and applied numerically to a variety of initial guesses. The correction to the nth guess of the source function is ~~(n)(r)=~ f0T [1-f(~)(t)~dt 1 laf(0)(r) 2 4 a~ where f is the flux and b is the source function, normalized so that f= 1. It is shown analytically that this method converges uniformly in the sense that the maximum error decreases with successive iterations. The method is insensitive to the initial guess; convergence is rapid for initial guesses that err by factors of 100. A numerical solution is presented which maintains the constancy of the flux to five parts in 106.
- Publication:
-
The Astronomical Journal
- Pub Date:
- 1963
- DOI:
- 10.1086/109128
- Bibcode:
- 1963AJ.....68S..74G