The non-linear saturation dynamics of TAEs (toroidicity-induced Alfvén eigenmodes) is investigated numerically in tokamaks and stellarators. Special attention is given to the influence that pitch-angle collisions among the fast ions have in the non-linear regime.For this investigation a perturbative model is used. We employ the 3D ideal reduced MHD eigenvalue code CKA to obtain the mode frequency and mode structure. This information is given to the non-linear gyro-kinetic particle-in-cell code EUTERPE, which calculates the growth rate of the mode and the temporal evolution of the mode amplitude. The mode structure remains fixed for the entire calculation.In the tokamak, analytical predictions regarding the transition from periodic non-linear behaviour to a steady-state solution and the scaling of the saturated amplitude are available. Both are influenced by collisions. The numerical results are in agreement with the theoretical predictions within the validity range of the theory (Berk et al 1992 Phys. Rev. Lett. 68 3563). Beyond the validity range of the theory different scaling laws are found numerically.We show that using a momentum-conserving collision operator does not change the scaling significantly for small ν, but is important for high collision frequencies.The stellarator case, a Wendelstein 7-X high-mirror configuration, shows some differences when compared with the tokamak. Most notably, the saturated perturbed magnetic field becomes a non-monotonic function of ν.