Convergence of the BE99 method in the time domain. In total 192 models with different initial values have been integrated. Parameters: T_e [K] = 8000, 9000, 10 000; $n_{\mathrm{e}}^{\mathrm{init}}[{\mathrm{cm}}^{-3}]=1000,2000,5000,10000$; $x_{\mathrm{e}}^{\mathrm{init}}=0.05,0.1,0.2,0.3$; $x_{\mathrm{N}}^{\mathrm{init}}=0.01,0.1$; $x_{\mathrm{O}}^{\mathrm{init}}=0.01,0.1$. Each black curve represents one model, where the BE99 method (assuming equilibrium) has been applied following the gas through the non-equilibrium state. For all these models the BE99 method measures the true gas conditions up to 5% accuracy (indicated as yellow horizontal stripe) after ∼10⁹ s.