Upper panel: RMS value of the Bz componentof the magnetic field produced by the Alfvén wave, as a function of time. The solid black linecorresponds to the analytical solution and the crosses are the numerical solution obtained with the STS scheme at order two. It can be seen there is good agreement with the analytical solution for all the diffusivities tested. Middle panel: relative error in time for the RMS value of Bz component. The red, green and blue lines are for the numerical solution given by the RK scheme working in the second, third and fourth order, respectively. The dashed lines corresponds to the solution obtained with the STS operator working also in second, third and fourth order. Lower panel: CRMSE in time for both schemes defined by Eq. (43). As we expect, the behaviour of both schemes is similar as it is shown by the CRMSE. The time axis is in the units of the crossing time τ = L∕cA and the dotted vertical lines mark the time where the L1-norm is calculated, t0 = 0.7τ.
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