Numerical solution for the mean intensity J_num as a function of optical depth τ (left column), relative deviation ΔJ_rel from the analytical solution as a function of optical depth τ (center column), and maximum relative deviation max(ΔJ_rel) as a function of iteration count (right column). The photon destruction probability ϵ ranges from 10^-1 (top row) to 10^-6 (bottom row). The dashed and dot-dashed lines in the left column and center column mark the optical surface at τ = 1 and the thermalization depth τ_therm. The dotted line in the center column indicates zero deviation. Dashed lines in the right column show the convergence speed for Gauss-Seidel corrections applied only during upsweeps, solid lines show the convergence speed for corrections applied during both upsweeps and downsweeps.