The theoretical part of this report shows that the second order modes become unstable for greater than . Nevertheless, saying that a mode is unstable is not equivalent to saying that the calculation will converge. For those values of we have a example of this behaviour. In fact a second order perturbation is effectively amplify but I can't say if the solution will converge or not. It's a particularity fo this zone. Sometimes the solution solution will converge and sometimes we have an example of chaotic system.
The figure 3.5 shows a converge solution.
The exact determination of the zone of convergence would be very hard, and has not been done in this project.