Late time growth is a serious defect of the time domain electromagnetic numerical methods. It has been reported in some conformal FDTD numerical codes; and it is also observed in our FDTD/FVTD hybrid numerical code. The paper is devoted to investigations leading to a stabilizing technique to eliminate the late time growth in our FDTD/FDTD or FDTD/FVTD hybrid. Since stability is related to the manner the boundary condition is approximated, we also present a boundary condition simulation. The scattering object in this investigation is smooth.