  Numerical solutions of the mode-coupling theory (MCT) equations for a
hard-sphere fluid confined between two parallel hard walls are elaborated. The
governing equations feature multiple parallel relaxation channels which
significantly complicate their numerical integration. We investigate the
intermediate scattering functions and the susceptibility spectra close to
structural arrest and compare to an asymptotic analysis of the MCT equations.
We corroborate that the data converge in the $\beta$-scaling regime to two
asymptotic power laws, viz. the critical decay and the von Schweidler law. The
numerical results reveal a non-monotonic dependence of the power-law exponents
on the slab width and a non-trivial kink in the low-frequency susceptibility
spectra. We also find qualitative agreement of these theoretical results to
event-driven molecular-dynamics simulations of polydisperse hard-sphere system.
In particular, the non-trivial dependence of the dynamical properties on the
slab width is well reproduced.
