Recently, an empirical model of the acceleration/deceleration of coronal mass ejections (CMEs) as they propagate through the solar wind was developed using near-Sun (coronagraphic) and near-Earth (in situ) observations <Gopalswamy et al., 2000, 2001a>. This model states and quantifies the fact that slow CMEs are accelerated and fast CMEs are decelerated toward the ambient solar wind speed (~400 km/s). In this work we study the propagation of CMEs from near the Sun (0.083 AU) to 1 AU using numerical simulations and compare the results with those of the empirical model. This is a parametric study of CME-like disturbances in the solar wind using a one-dimensional, hydrodynamic single-fluid model. Simulated CMEs are propagated through a variable ambient solar wind and their 1 AU characteristics are derived to compare with observations and the empirical CME arrival model. We were able to reproduce the general characteristics of the prediction model and to obtain reasonable agreement with two-point measurements from spacecraft. Our results also show that the dynamical evolution of fast CMEs has three phases: (1) an abrupt and strong deceleration just after their injection against the ambient wind, which ceases before 0.1 AU, followed by (2) a constant speed propagation until about 0.45 AU, and, finally, (3) a gradual and small deceleration that continues beyond 1 AU. The results show that it is somewhat difficult to predict the arrival time of slow CMEs (Vcme 1000 km/s) has a smaller dispersion so the prediction can be more accurate.