Hall test, showing in the upper panel the time evolution for the numerical and analytical solutions of the B_z components of the magnetic field fluctuations due to the precession of the plane-polarised Alfvén wave in a fixed spacial point (x = 0). The solid line represents the analytical solution and the red crosses are the numerical solution. Middle panel: relative error of the numerical solution respect the analytical solution for both the RK and the HDS schemes, solid lines and dashed lines respectively. Lower panel: CRMSE in time for the B_z component. It can be seen how the two schemes have an almost identical behaviour in time and with the order. This it is expected because the HDS operator works as a RK operator. Also this shows us how well performs the Strang splitting.