[SciPy-Dev] ode and odeint callable parameters

[Marcel Oliver]

Benny Malengier writes:
 > This somewhat proves that returning output also on wrong output (not
 > satisfying atol/rtol) like ode.integrate does is not a good practice. In the
 > above case, with scipy.ode, you should test for r1.successful() after every
 > integrate, which you failed to do.

I totally agree.  In fact, I used this example to teach students to be
critical about solver output.  We tested with a number of solvers -
not just library solvers, mostly simple self-written ones - and all of
failing ones except dop853 fail catastrophically on this example.

So in some sense the dop853 has the worst possible behavior, but on
the other hand I am still amazed how close it is (qualitatively) to
the correct solution.  And dop853 does very well for non-stiff
problems.  In particular, it is only very mildly dissipative on energy
conserving systems.

 > With the odes scikit approach, wrong output just stops the solve routine and
 > goes to sol.errors. The dopri warning output is to increase nsteps. If you do
 > that, and restart at the last computed solution, the error of dop853 becomes:
 >   UserWarning: dop853: problem is probably stiff (interrupted)
 > So an indication to use another solver.

Interesting, I guess I never increased nsteps that much.  I absolutely
agree that an explicit fail is much better.

Best,
Marcel