We have found that the conventional generic dynamical model for gamma-ray bursts ( GRBs ) can not reproduce the Sedov solution in the non-relativistic limit .
Based on our refined generic dynamical model , we investigate afterglows from jetted GRB remnants numerically .
Many new results are reached .
For example , we find no obvious break in the optical light curve during the relativistic phase itself .
But an obvious break does exist at the transition from the relativistic phase to the non-relativistic phase , which typically occurs at time 10 to 30 days .
It is very interesting that the break is affected by many parameters , such as the electron energy fraction , \xi _ { e } , the magnetic energy fraction , \xi _ { B } ^ { 2 } , the initial opening angle of the jet , \theta _ { 0 } , and the medium density , n .
We also find that afterglows from jetted GRB remnants are uniformly characterized by a quick decay during the non-relativistic phase , with power law timing index greater than 2.1 .
Afterglows from GRB 970228 , 980326 , 980519 , 990123 , 990510 and 991208 can be satisfactorily fitted if the corresponding GRB ejecta are highly collimated .