A novel methodology is presented that combines short-cut methods and efficient numerical algorithms to enhance the efficiency of numerical simulation of forced cyclic fixed-bed processes and to improve the insight about their advantages. It is shown that the model of a forced cyclic process can be approximated by a continuous process model featuring qualitatively equivalent behavior. This model reduction is exact for infinitesimally small cycle periods. Using this limiting case as a generic pattern, we derive two algorithms for computing the periodic state. The first algorithm is based on a linear expansion around the zero-order solution. A considerable advantage of the method is its compatibility with adaptive solvers for the underlying PDAE-systems. The second exploits the dominant role of dispersive effects on the zero-order solution. The resulting low-dimensional spectrum of significant eigenvalues is mapped to a coarse-grid representation of the periodic solution, reducing the computational effort by one order of magnitude compared to standard methods. This low-dimensional representation of the system is most advantageous in the computation of bifurcation diagrams. The advantages of the proposed methods are illustrated by simulations of the cyclic operation of two systems, a regenerative heat exchanger and a reverse-flow reactor. (C) 2013 Elsevier Ltd. All rights reserved.