  We present theoretical foundations and numerical demonstration of an
efficient method for performing time-dependent many-electron simulations for
electronic transport. The method employs the concept of stroboscopic wavepacket
basis for the description of electrons' dynamics in the semi-infinite leads.The
rest of the system can be treated using common propagation schemes for finite
electronic systems. We use the implementation of our method to study the
time-dependent current response in armchair graphene nano-ribbons (AGNR) with
sizes up to 800 atoms described within tight-binding approximation. The
character of the time-dependent current is studied for different magnitudes of
the bias voltage, variable width and length of AGNRs, different positions of
the current measurement, and for full and reduced coupling of the AGNRs to the
electrodes.
