Governing equations describing the pressure swing adsorption processes with strong adsorbates were converted into dimensionless forms. The characteristic scales reflecting the system dimensions, operating conditions and physical properties including the isotherms indicated that the gas-phase convection mass transfer balances the adsorbent-phase mass accumulation. The gas-phase accumulation should not be considered a dominant mass transfer mode and would change rapidly with time. In order to avoid stiffness of time derivatives of the gas-phase accumulation and to obtain robust numerical solutions through the diagonally dominant matrices, the two leading terms should coexist in the difference equation. Through the present numerical strategy the convergence of the numerical integration and the accuracy of the simulated results were guaranteed for a wide range of time discretization. The algorithm was found to successfully predict the reasonable behaviors of process variables even for non-isothermal operations. (C) 2004 Elsevier Ltd. All rights reserved.