Theory of the N-Body Problem
June 9, 1996
22
Even though the Lipschitz conditions says that there can be only one true answer,
the unavoidable errors due to discretization and rounding make it is hard to tell which of
several outcomes is really the "correct" one, or even if any of them are correct. If the
"correct" outcome can not be obtained, then a choice must be made between which types
of deviations are better or worse than other.
As a result, I have had to based my judgements of which methods are "better" by
looking at the types of errors that I see and comparing them with other methods that have
a smaller step size. If several different methods all agree that a particular star system
should end up a certain way when a very small step size is used, then this information can
be used to judge the methods when they use a larger step size. So the definition of accu-
racy that I have had to use is:
Definition:
One method is more
accurate
than another if the results seem to
more closely match the results of several other methods when they
used "substantially" smaller step sizes, or more cpu time or both.
Signs that a method has the types of errors that I don't like cause
that method to be downgraded.
This is not the rigorous, technical definition that I would like to have used, but I
know of no better definition.
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