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There are some dozen supernovae (SNe) associated with long Gamma-ray bursts(GRBs) have been confirmed. Most of previous studies derive the physicalproperties of the GRB-SNe by fitting the constructed (psuedo-)bolometric lightcurves. However, many GRB-SNe have only a few filter data, for which the(psuedo-)bolometric light curves are very difficult to be constructed.Additionally, constructing (psuedo-)bolometric light curves rely on someassumptions. In this paper, we use the multi-band broken power-law plus$^{56}$Ni model to fit the multi-band light curves of the afterglows and theSNe (SN~2001ke, SN~2013dx, and SN~2016jca) associated with three GRBs(GRB~011121, GRB~130702A, and GRB~161219B). We find our model can account forthe multi-band light curves of the three GRB-SNe (except for the late-time$z-$band light curves of two events), indicating that the model is a reliablemodel. The $^{56}$Ni masses we derive are higher than that in the literature.This might be due to the fact that the $^{56}$Ni masses in the literature areusually obtained by fitting the psuedo-bolometric light curves whoseluminosities are usually (significantly) underestimated. We suggest that themulti-band model can not only be used to fit the multi-band light curves ofGRB-SNe that have many filter observations, but also fit those having sparsedata.

Modeling the Multi-band Light Curves of the Afterglows of Three Gamma-Ray Bursts and Their Associated Supernovae