The aim of this paper is to present a limited memory iterative method, called the Broyden Rank Reduction method, to simulate periodically forced processes in plug-flow reactors with radial gradients taken into account. The simulation of periodically forced processes in plug-flow reactors leads to the development of partial differential equations that are normally solved in time using dynamical simulation. Depending on the convergence properties of the system at hand, the number of cycles that needs to be computed up to a cyclic steady state is reached can be large. Therefore direct iterative methods are essential in order to capture the long time dynamics of such systems. In order to overcome severe memory constraints many authors have reverted to pseudo-homogeneous ID models and to coarse grid discretization, which renders such models inadequate or inaccurate. The results that we present show that the long time dynamics actually depends on the radius of the reactor and, hence, the full 2D model is essential in order to simulate periodically forced processes in plug-flow reactors accurately. (c) 2006 Elsevier Ltd. All rights reserved.