We use a series of cosmological N-body simulations and various analytic models to study the evolution of the matter power spectrum in real space in a Lambda Cold Dark Matter universe. We compare the results of N-body simulations against three analytical model predictions; standard perturbation theory, renormalized perturbation theory, and the closure approximation. We include the effects from finite simulation box size in the comparison. We determine the values of the maximum wavenumbers, k^{lim}_{1%} and k^{lim}_{3%}, below which the analytic models and the simulation results agree to within 1 and 3 percent, respectively. We then provide a simple empirical function which describes the convergence regime determined by comparison between our simulations and the analytical models. We find that if we use the Fourier modes within the convergence regime alone, the characteristic scale of baryon acoustic oscillations can be determined within 1% accuracy from future surveys with a volume of a few h^{-3}Gpc^3 at zsim1 or zsim3 in the absence of any systematic distortion of the power spectrum.
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