The full numerical solutions of the time-convolutionless modecoupling theory (TMCT) equation recently proposed by Tokuyama are compared with those of the ideal mode-coupling theory (MCT) equation based on the Percus-Yevick static structure factor for hard spheres qualitatively and quantitatively. The ergodic to non-ergodic transition at the critical volume fraction φc predicted by MCT is also shown to occur even for TMCT. Thus, φc of TMCT is shown to be much higher than that of MCT. The dynamics of coherent-intermediate scattering functions and their two-step relaxation process in a β stage are also discussed
