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In order to investigate how the time-convolutionless mode-coupling theory(TMCT) recently proposed by Tokuyama can improve the critical point predictedby the ideal mode-coupling theory (MCT), the TMCT equations are numericallysolved based on the Percus-Yevick static structure factor for hard spheres as apreliminary test. Then, the full numerical solutions are compared with those ofMCT for different physical quantities, such as intermediate scatteringfunctions and diffusion coefficients. Thus, the ergodic to nonergodictransition 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 $q_c\sigma_d=20$ forTMCT, 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 byMCT is also discussed.

Preliminary test of time-convolutionless mode-coupling theory based on the Percus-Yevick static structure factor for hard spheres