Time-dependent evolution of a Strömgren sphere in a hydrogen gas (n = 10 cm^-3, T = 7500 K) surrounding a hot star described by a blackbody radiator with an effective temperature of 40 000 K and a radius of 9 solar radii for different values of the parameter f which controls the time step size (cf. Eq. (15)). As is shown, the simulated expansion of the ionization front becomes slower for increasing time steps, and the analytic solution for the expansion of the ionization front described by Eq. (31) (black line) is for a value of f = 0.1 quite well represented by our simulation (red curve).