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We numerically simulate the gamma-ray burst (GRB) afterglow emission with aone-zone time-dependent code. The temporal evolutions of the deceleratingshocked shell and energy distributions of electrons and photons areconsistently calculated. The photon spectrum and light curves for an observerare obtained taking into account the relativistic propagation of the shockedshell and the curvature of the emission surface. We find that the onset time ofthe afterglow is significantly earlier than the previous analytical estimate.The analytical formulae of the shock propagation and light curve for theradiative case are also different from our results. Our results show that evenif the emission mechanism is switching from synchrotron to synchrotronself-Compton, the gamma-ray light curves can be a smooth power-law, whichagrees with the observed light curve and the late detection of a 32 GeV photonin GRB 130427A. The uncertainty of the model parameters obtained with theanalytical formula is discussed, especially in connection with the closurerelation between spectral index and decay index.

Temporal Evolution of the Gamma-ray Burst Afterglow Spectrum for an Observer: GeV--TeV Synchrotron Self-Compton Light Curve