Can you provide a jargon-free (as much as possible) explanation of what is meant by "dense ODE systems", and "sparse ODE systems"?
Some hints I have gotten from Googling:
dense ODE systems' computation cost increases quadratically with the size of the system
sparse ODE systems' computation cost does not correlate with the size of the system
dense ODE systems' computation cost is dominated by CPU considerations
sparse ODE systems' computation cost is dominated by "communication" considerations
Some guesses of mine: if a dense ODE system's computation cost increases quadratically with the size of the system, then there must be lots of "point-point" interactions between the variables. So, would an n-body problem be dense?
I can't think of a good example of a sparse ODE system, except for the trivial one, where I take a bunch of independent ODEs which have nothing to do with each other, and then put them together claiming it is a "system"?
Why would a sparse ode system's computation cost be dominated by communication concerns? Communication between what? Processors?