We present four different numerical methods for the numerical simulation of simulated moving bed chromatography. Two approaches use fixed-point iteration for computing cyclic steady states, and two other approaches use operator splitting for computing complete system trajectories. All methods are based on weak coupling of individual column models and can easily be implemented using any existing single-column solver. Simulation software is implemented based on the CADET project and published as open source code. The numerical performance is compared using five case studies. For both fixed-point iteration and operator-splitting, an alternative approach is found to be more efficient than the standard approach. Namely, the one-column analog saves time in computing the cyclic steady state, while lag-aware operator-splitting yields more detailed information on the system trajectory. The presented methods can be combined with other models, for example to consider hold-up volumes, and have applications beyond simulated bed chromatography. (c) 2018 Elsevier Ltd. All rights reserved.