[SciPy-User] Error estimation when using solve_ivp

[David Hagen]

The adaptive solvers ensure that the error at each step is less than rtol
in relative terms or atol in absolute terms. A conservative estimate of the
total error in any states at the end would be these numbers times the
number of steps required to solve the system. In my experience, this is a
very rough estimate for adaptive solvers; so when I start working on a new
problem, I typically run an example of the problem at a crazy strict
tolerance (as low as will finish in reasonable time) and then compare these
gold standard results to looser and looser tolerances so I have a better
idea of how far off a less accurate solution actually is.
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