  In order to investigate how the time-convolutionless mode-coupling theory
(TMCT) recently proposed by Tokuyama can improve the critical point predicted
by the ideal mode-coupling theory (MCT), the TMCT equations are numerically
solved based on the Percus-Yevick static structure factor for hard spheres as a
preliminary test. Then, the full numerical solutions are compared with those of
MCT for different physical quantities, such as intermediate scattering
functions and diffusion coefficients. Thus, the ergodic to nonergodic
transition predicted by MCT is also found at the critical volume fraction
$\phi_c$ which is higher than that of MCT. Here $\phi_c$ is given by
$\phi_c\simeq 0.5817$ at $q_c\sigma_d=40$ and 0.5856 at $q_c\sigma_d=20$ for
TMCT, while $\phi_c\simeq 0.5159$ at $q_c\sigma_d=40$ and 0.5214 at
$q_c\sigma_d=20$ for MCT, where $q_c$ is a cutoff of wave vector and $\sigma_d$
a particle diameter. The same two-step relaxation process as that predicted by
MCT is also discussed.

Statistical Mechanics