Analytical and numerical comparison of a synchrotron cooling problem and the impact of grid resolution. Top panel: comparison of numerical (solid colored lines) and analytical (dashed black line) solutions for synchrotron cooling electrons in a spherical blob with a constant magnetic field. Each numerical result was calculated using a different number of grid points per decade in the electron Lorentz factor (n_ppd) as indicated in the legend (see also markers in the top panel of Fig. 1). Bottom panel: Ratio χ between the numerical and the analytical solutions.