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I always wonder what "battle tested" means. Even very high-order Runge-Kutta solvers may fail to preserve simple qualitative properties such as having a linear
by thanatropism 8y ago
I always wonder what "battle tested" means.
Even very high-order Runge-Kutta solvers may fail to preserve simple qualitative properties such as having a linear oscillator stay in its phase space. Meaning: simulations of physical systems will typically diverge unless you're very lucky. Might mean a satellite failing to enter stable orbit. Solvers for systems with certain specific phase space properties may be found (for satellites there are particular solvers), but do you always know beforehand what you're dealing with?
This "numerical power will solve every problem" attitude is bound to lead us to disaster. But then, so was the "ORM will solve every problem" attitude, for example. Luckily we have people actively researching symbolic computation. Jeez, without symbolic computation finding very high-order Runge-Kutta methods is exceedingly hard and error-prone.
- donquichotte 8y agoSymbolic integration requires an accurate model of the system, whereas you can throw numerical methods at most problems and get results that are good enough. If you worry about your satellite falling down you can always try energy-preserving integrators. I would wager the guess that most PID controllers, arguably the most common application of numerical integration, work just fine with just basic forward Euler integration.
- thanatropism 8y agoI can't disagree with your reply because it seems we're living in entirely different planets. It's a good thing that we don't have to develop a full-scale polemic (I was thinking sociologists and economists, but heck look at Taleb the professional polemist) since the world can reward us both for adding value as technologists and engineers.