Newton Game Dynamics :
as for PhysX I don't know, but most of the popular physics engines use iterative solvers (bullet, havok) your 'one stage' definition matches an iterative solver.Our engine implements a deterministic solver, which is not based on traditional LCP or iterative methods, but possesses the stability and speed of both respectively. This feature makes our product a tool not only for games, but also for any real-time physics simulation.
As for the 'two stage' defintion then you're looking at, as mentioned above, LCP based solvers (Linear complementary problem). LCP is a broad term for certain classes of co-dependent mathematical problems (think quadratic equations) such as for instance, physics solvers.
So an iterative solver achieves a higher degree of accuracy through progressive refinement (think tight collisions between 3 or more objects) where are a non iterative solver (not that I know any specifics) uses various mathmatical tools developed for thermodynamic problems to, I assume, produce close approximates as an alternative.
In the words of Newton (game dynamics, not the man) I should imagine that the best physics engines use a wide combination of cross discipline techniques.
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