  In this work, we present an extensive computational study on the
Ziff-Gulari-Barshad (ZGB) model extended in order to include the spatial
diffusion of oxygen atoms and carbon monoxide molecules, both adsorbed on the
surface. In our approach, we consider two different protocols to implement the
diffusion of the atoms/molecules and two different ways to combine the
diffusion and adsorption processes resulting in four different algorithms. The
influence of the diffusion on the continuous and discontinuous phase
transitions of the model is analysed through two very well established methods:
the time-dependent Monte Carlo simulations and the steady-state Monte Carlo
simulations. We also use an optimization method based on a concept known as
coefficient of determination to construct color maps and obtain the phase
transitions when the parameters of the model vary. This method was proposed
recently to locate nonequilibrium second-order phase transitions and has been
successfully used in both systems: with defined Hamiltonian and with absorbing
states. The results obtained via time-dependent Monte Carlo simulation along
with the coefficient of determination are corroborated by traditional
steady-state Monte Carlo simulations also performed for the four algorithms.
Finally, we analyse the finite-size effects on the results, as well as, the
influence of the number of runs on the reliability of our estimates.
