On the accuracy of the ALI method for solving the radiative transfer equation

Abstract

We solve the integral equation describing the propagation of light in an isothermal plane-parallel atmosphere of optical thickness $\tau^*$, adopting a uniform thermalization parameter $\epsilon$. The solution given by the ALI method, widely used in the field of stellar atmospheres modelling, is compared to the exact solution. Graphs are given that illustrate the accuracy of the ALI solution as a function of the parameters $\epsilon$, $\tau^*$ and optical depth variable $\tau$.