  Rapid processes of heat transfer are not described by the standard heat
conduction equation. To take into account a finite velocity of heat transfer,
we use the hyperbolic model of heat conduction, which is connected with the
relaxation of heat fluxes. In this case, the mathematical model is based on a
hyperbolic equation of second order or a system of equations for the
temperature and heat fluxes. In this paper we construct for the hyperbolic heat
conduction equation the additive schemes of splitting with respect to
directions. Unconditional stability of locally one-dimensional splitting
schemes is established. New splitting schemes are proposed and studied for a
system of equations written in terms of the temperature and heat fluxes.

Numerical Analysis