Upper panel: CRMSE values at t = 5τ s for different values of the pair (N_STS, ν). The horizontal dashed lines corresponds to the RK scheme values. The symbols correspond to the STS scheme, each of them indicate a different value of ν. The black, red, green and blue colours indicate first, second, third and fourth order accuracy respectively. The dotted lines linking the symbols are drawn just to make the plot more readable. Middle panel: CPU time spend by the schemes to reach the same point in the simulations. The colour and symbol code is the same as the upper panel. Lower panel: order computed using the L₁ -norm at t₀ = 0.7τ, see the dotted vertical line in Fig. 5; again, the colour and symbol code is the same as the upperpanel. In subfigure (a), we have a case with low ambipolar diffusion where the first order results unstable and the errors for the STS scheme are very close to the RK values. In this case, we have no acceleration because the system is out of the STS regime and the time increase linearly with N_STS as expected.