Time evolution of the absolute relative error of the growth time scale ω measured in the simulation for a line-mass of f_cyl = 0.25. The solid blue, cyan, and orange line shows the error of the density, x-acceleration and x-velocity, respectively. We define the beginning of the non-linear evolution by determining the point in time when the error exceeds a value of 5% when measuring back from the end of the simulation. The thresholds are indicated by the vertical dashed-dotted lines, for which we also determine the line-masses at the position of the core, which are given in the legend.