Calculation of the Electron Self-Energy for Low Nuclear Charge

We present a nonperturbative numerical evaluation of the one-photon electron self-energy for hydrogenlike ions with low nuclear charge numbers $Z=1\mathrm{}$ to 5. Our calculation for the $1S$ state has a numerical uncertainty of 0.8 Hz for hydrogen and 13 Hz for singly ionized helium. Resummation and convergence acceleration techniques that reduce the computer time by about 3 orders of magnitude were employed in the calculation. The numerical results are compared to results based on known terms in the expansion of the self-energy in powers of $Z\alpha$.