Comparison of the output of the pseudo-spectral approach (dashed line) and the semi-analytical solution obtained using the explicit approach (continuous line) for magnetic field model II. The solution from the pseudo-spectral approach uses a polynomial fit for the relevant background radial profiles. From top to bottom: (a) χ_n, (b) χ_c, (c) v_n, r, and (d) v_ad, r. All quantities are in code units, plotted as functions of r for θ = π/3 and θ = π/2.