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The stability analysis is presented for the finite-difference time-domain modeling of a Lorentz dielectric. In particular this study is focused on the Young scheme that employs the polarizability and the polarization current for the representation of the Lorentz permittivity, and collocates temporally the magnetic field with the polarization current. The Routh criterion is employed for the stability limit determination. The necessary conditions that ensure stability are thoroughly derived for the general as well as for limiting cases.