Propagation of chemical waves in the Belousov-Zhabotinsky (BZ) reaction-diffusion system is simulated with an improved Oregonator-type model in the entire region of propagation of solitary waves. The dependence of wave speed on bromate concentration and acidity is determined. Deviations from linear dependence of the speed on the quantity theta(0.5) = (h(0)([HBrO3] + [BrO3-]))(0.5) (h(0) = Hammett acidity function) are found at both high and low theta. The model predicts that the wave speed has a maximum at high values of theta. Comparison of experimental data with simulations shows that saturation of the reactive layer by oxygen can significantly increase the region in parameter space that supports propagation of solitary waves.