Verification of analytical derivation for T_∞/T₀ = 0.01. Comparison as a function of χt for a simulation in Python (blue markers), as well as the zeroth-order (magenta curve) and first-order solutions (three green curves). In the top panel, the absolute reduction of max[T_Tot] and widening of HWHM (R_0.5) is shown. In the following two panels, the difference to the simulation is shown for the peak temperature and width, respectively. These panels also include the evolution of ϕ_∞/ϕ₀ in black. The dashed vertical line marks t = 1/χ and the dotted vertical line marks t = t’ >> 1/χ, the time of the snapshot in Fig. 3b.