We numerically simulate the gamma-ray burst (GRB) afterglow emission with a one-zone timedependent code. The temporal evolutions of the decelerating shocked shell and energy distributions of electrons and photons are consistently calculated. The photon spectrum and light curves for an observer are obtained taking into account the relativistic propagation of the shocked shell and the curvature of the emission surface. We find that the onset time of the afterglow is significantly earlier than the previous analytical estimate. The analytical formulae of the shock propagation and light curve for the radiative case are also different from our results. Our results show that even if the emission mechanism is switching from synchrotron to synchrotron self-Compton, the gamma-ray light curves can be a smooth power-law, which agrees with the observed light curve and the late detection of a 32 GeV photon in GRB 130427A. The uncertainty of the model parameters obtained with the analytical formula is discussed, especially in connection with the closure relation between spectral index and decay index.

The ejected material at the binary neutron star merger GW 170817 was confirmed as a kilonova by UV, optical, and IR observations. This event provides a unique opportunity to investigate the particle acceleration at a mildly relativistic shock propagating in the circumbinary medium. In this paper, we simulate the nonthermal emission from electrons accelerated by the shock induced by the kilonova ejecta with a time-dependent method. The initial velocity and mass of the ejecta in the simulations are obtained from the kilonova observations in GW 170817. If the ambient density is high enough (≥ 10 −2 cm −3 ), radio, optical/IR, and X-ray signals will be detected in a few years, though the off-axis short gamma-ray burst models, accounting for the X-ray/radio counterpart detected at ∼ 10 days after the merger, implies low ambient density. We also demonstrate that the additional low-mass (∼ 10 −5 M ⊙ ) component with a velocity of 0.5c-0.8c can reproduce the early X-ray/radio counterpart. This alternative model allows a favorably high density to detect the nonthermal emission due to the kilonova ejecta. Even for a low ambient density such as ∼ 10 −3 cm −3 , depending on the microscopic parameters for the electron acceleration, we can expect a growth of radio flux of ∼ 0.1 mJy in a few years.