Cosmos uses what iterative scheme for large displacement in static studies?

I don't know how it works with nonlinear Cosmos, but for a linear static study with large displacement activated the loads are applied gradually in steps up to their full values. The number of steps is chosen by Cosmos based on the full load applied at once displacement results.

Edit:

The standard version of Cosmos cannot perform nonlinear studies.

as far as I am aware it is a force controlled autostepping solution using the Newton Raphson method.