A numerical method based on finite differences is proposed for simulating pressure swing adsorption processes with intraparticle diffusion controlling. The problem has two important spatial coordinates : the axial position in the bed and the location within a particle. The method proposed keeps the two coordinate scales separate. Diffusion equations with variable main- and cross-term diffusivities are solved implicitly for the particles at each time step and the solution is expressed in terms of the bed-scale variables. The material balances on the bed can then be solved with the bed-scale variables as the only unknowns. The method is computationally efficient and validated by comparison with an exact solution derived under conditions of plug how, constant total pressure, and with a binary Langmuir isotherm. As a full example, we treat the kinetic separation of air to produce nitrogen using a fixed bed of carbon molecular sieve. Characteristics of the specific implementation are incorporation of variable-step grids with identical volumes for the intraparticle diffusion equations and the use of the third-order QUICK scheme to discretize the convection terms in the material balances for the bed.