  We describe new functionality in the GYRE stellar oscillation code for
modeling tides in binary systems. Using a multipolar expansion in space and a
Fourier-series expansion in time, we decompose the tidal potential into a
superposition of partial tidal potentials. The equations governing the
small-amplitude response of a spherical star to an individual partial potential
are the linear, non-radial, non-adiabatic oscillation equations with an extra
inhomogeneous forcing term. We introduce a new executable, gyre_tides, that
directly solves these equations within the GYRE numerical framework. Applying
this to selected problems, we find general agreement with results in the
published literature but also uncover some differences between our direct
solution methodology and the modal decomposition approach adopted by many
authors.
  In its present form gyre_tides can model equilibrium and dynamical tides of
aligned binaries in which radiative diffusion dominates the tidal dissipation
(typically, intermediate and high-mass stars on the main sequence). Milestones
for future development include incorporation of other dissipation processes,
spin-orbit misalignment, and the Coriolis force arising from rotation.
