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In the dynamical models of gamma-ray burst (GRB) afterglows, the uniformassumption of the shocked region is known as provoking total energyconservation problem. In this work we consider shocks originating frommagnetized ejecta, extend the energy-conserving hydrodynamical model of Yan etal. (2007) to the MHD limit by applying the magnetized jump conditions fromZhang & Kobayashi (2005). Compared with the non-conservative models, ourLorentz factor of the whole shocked region is larger by a factor$\lesssim\sqrt{2}$. The total pressure of the forward shocked region is higherthan the reversed shocked region, in the relativistic regime with a factor ofabout 3 in our interstellar medium (ISM) cases while ejecta magnetizationdegree $\sigma<1$, and a factor of about 2.4 in the wind cases. For $\sigma\le1$, the non-conservative model loses $32-42$% of its total energy for ISMcases, and for wind cases $25-38$%, which happens specifically in the forwardshocked region, making the shock synchrotron emission from the forward shockless luminous than expected. Once the energy conservation problem is fixed, thelate time light curves from the forward shock become nearly independent of theejecta magnetization. The reverse shocked region doesn't suffer from the energyconservation problem since the changes of the Lorentz factor are recompensed bythe changes of the shocked particle number density. The early light curves fromthe reverse shock are sensitive to the magnetization of the ejecta, thus are animportant probe of the magnetization degree.

An energy-conserving dynamical model of GRB afterglows from magnetized forward and reverse shocks