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i think the standard ode solver is O(n*n*n) and newton is O(n*n) worst case so newton currently is faster aswell! there is a new ode solver in the works which is O(n)

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Newton solver goes for acuracy rather than speed. The statistic order of the newton solver is best case linear O(N), worst case quadratic O(N*N). on average you get 0(N * log(N)). Where N is the number of restrited DOF.

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I've done all manner of physics simulations and I admit my statistics are weak, but the above makes little sense to me. The Statistic Order is a SORTING techinique and those numbers somewhat represent diffrent how many diffrent comparasons are done until you get the result you were searching for. So I'm gathering they are sorting the DOF and then what, applying a physics update based on this sort? From my ignorance or their lack of facts, I just don't see where the claims of "accuracy" or "speed" are based on.

I've done runge-kutta integration, monte-carlo simulations, set up terabyte lattices, and even had a brief stint with quantum computing, but I've never done anything like a game physics engine, so the above I'm at a loss as to what the number above mean.

Long story short, I don't see how these arguments prove anything about speed since I don't understand how sorting and numerically integrating are related. I could make a million guesses related to matrices, taylor series expansion cut off, etc, but thats all PHysics and not game ODE, so could someone give me some insight as to what the above means?