Application of the generalized newton-raphson method to the singly-ionized calcium line formation problem in model stellar atmospheres. Doctoral thesis

A new method is proposed for solving the statistical equilibrium and radiative-transfer equations for the level populations of a multilevel model atom in a model stellar atmosphere. These two sets of equations are reduced to a single system of nonlinear operator equations by incorporating the integral form of the radiative transfer equations into the equations of statistical equilibrium. An iterative procedure for solving the system based on the Generalized Newton-Raphson (GNR) method is described and compared to other methods currently being used to solve such problems. The GNR method eliminated the possibility of convergence to inconsistent solutions and, in certain test cases, reduced the number of iterations necessary to reach convergence by as much as an order of magnitude