Two new techniques for single-vessel Pressure or Vacuum Swing Adsorption (P-VSA) mathematical models are presented that improve convergence stability to Cyclic Steady State (CSS) when Pressure Equalization (PE) steps are involved. The first method, the Reflected Equalization Pressure (REP) method uses simplifying assumptions to derive a simple and efficient analytical solution for the unknown pressure profile boundary condition (BC) to use during PE steps on the first simulated cycle of a P-VSA simulation without the need for user defined functions or additional ODEs. The second method, the Weighted Store-and-Retrieve (WSR) method is a variation on the Traditional Store-and-Retrieve (TSR) method for simulating PE steps where gases flow from one vessel to another in a single-vessel mathematical model. The WSR method retains history across several cycles, passing this back into the mathematical model via weighting factors to average the data and dampen the oscillatory response of a mathematical model to PE steps. Several examples of this technique are applied to the O-2 VSA and H-2 PSA systems. (C) 2019 Elsevier Ltd. All rights reserved.