The stellar atmospheres problem

Abstract This paper discusses the construction of model stellar atmospheres placing particular stress on the mathematical methods used. The basic equations and assumptions of the problem are presented. Techniques which reduce the transfer equation to a set of linear equations are developed. It is shown how the constraint of radiative equilibrium may then be included directly into the transfer equation, yielding much more powerful methods for constructing model atmospheres than previously available. The scheme where all equations and constraints are solved simultaneously via full linearization is also given,and possibilities for improvement are briefly discussed.