  We present a combined analytical and numerical approach based on the Mori
projection operator formalism and Monte Carlo simulations to study surface
diffusion within the lattice-gas model. In the present theory, the average jump
rate and the susceptibility factor appearing are evaluated through Monte Carlo
simulations, while the memory functions are approximated by the known results
for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for
collective diffusion, while approximate correlation effects beyond DMF are
included for tracer diffusion. We apply our formalism to three very different
strongly interacting systems and compare the results of the new approach with
those of usual Monte Carlo simulations. We find that the combined approach
works very well for collective diffusion, whereas for tracer diffusion the
influence of interactions on the memory effects is more prominent.
