  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 z\sim1 or z\sim3 in the absence of any
systematic distortion of the power spectrum.
