Residual norm of the rate equations (six-level HI setup) as a function of the population change norm for the JFNK (blue) and RH92 (red) schemes. The Krylov relative tolerance was set to 10⁻². The population densities were initialized using the zero radiation approximation. Each solver was run in order to achieve several Newton relative tolerances in the population change norm (e.g., 10⁻¹, 10⁻²). We then recorded the final residual and population change norms.