Numerical methods in radiative transfer

Abstract

This chapter considers a selection of numerical methods developed since 1960s for solving radiative transfer (RT) problems in stellar atmospheres and in all other diluted media where nonlocal thermodynamic equilibrium (NLTE) effects are important. Special emphasis is put on the solution of the radiative transfer equation (RTE) when the source function is given, because its so-called formal solution constitutes a necessary step in any iterative procedure for the solution of more general RT problems. The application of different methods to the spectral line formation problem, which requires the self-consistent solution of the RTE for the line(s) radiation field and the statistical equilibrium (SE) equation(s) for the atomic-level populations involved, is discussed for both linear and nonlinear problems.