Numerically Stable Discrete Ordinate Solutions of the Radiative Transfer Equation

Abstract

A new numerically stable and highly accurate method for the computation of the radiation field in a spectral line is presented. It involves the following three main steps: First by means of a discretisation of the angle and frequency space the transfer equation is transformed into a system of coupled first order differential equations. Next the system is solved analytically and finally it is cast into a form, which gives the emergent intensities as a function of the inflowing radiation and which contains only negative eigenvalues (assuring a numerically benign behaviour). We give the condition for closed solutions and discuss the versatility, accuracy and numerical performance of this approach.