Top row: log-log representation of the global error in the emergent intensity profile as a function of the number of grid-points. Bottom row: local error as a function of the spatial coordinate s ∈ [0, 100] for a sampling of 50 equispaced grid points for a single wavelength near the line core. The four columns correspond to four different atmospheric models, where the absorption coefficient χ_ν and emissivity ϵ_ν are given, respectively, by Eqs. (20) and (21) (first column), by Eqs. (22) and (23) (second column), by Eqs. (24) and (25) (third column), and by Eqs. (26) and (27) (fourth column). The parameters are: c₁ = 0.01, c₂ = 0.05, c₃ = 0.15, k₁ = 1/25, k₂ = 1/15, k₃ = 5, j₁ = 2, j₂ = 20, s_d1 = 39.985, and s_d2 = 39.955. This choice of s_d1 and s_d2 warrants a monotonic approach of the grid points to the location of the discontinuity (or sharp gradient) as the grid sampling is refined. The global and the local error are computed as exposed in Eqs. (A.1) (considering the Stokes I component only) and (A.2), respectively, with a reference atmospheric model with 10⁴ grid points.