The optimization of simulated moving bed systems is a complex task, and one of the difficulties is the lack of simulation methods that are sufficiently accurate and fast to be incorporated in the optimization algorithms. This paper presents a simulation of an adsorption column with finite differences based on a Lagrangian approach. The results obtained with this integration method were compared to values reported in the literature; the comparison shows that the accuracy of the integration method is not lower than that obtained with published methods and that this integration method requires a much lower cost in computation time. Various simulations were compared with experimental data for injections of caffeine and sodium 2-naphthalenesulfonate and with published results for the separation of isomers of omeprazole. The effects of axial diffusion and resistance to mass transfer on the elution curves were studied, and the simulation results were compared with the known theoretical analytical solution for a linear isotherm.