Mauro

Thanks for the clarification (I think you should open an issue with the test case you posted to julia-users). Doing it the other way will need some careful designing of...

Could use or take inspiration from: https://github.com/spencerlyon2/IterationManagers.jl

Sorry to not have looked at this yet! I'll try over the next few days, but I suspect I may well not be able to give much input until mid-January.

I had a brief look over it: looks good. A few comments in-line, probably redundant as this is still WIP. To test performance, maybe use https://github.com/mauro3/IVPTestSuite.jl: Threebody and HIRES should...

Actually, above points about "sophisticated dense output" and multistep methods may need the same solution: a state which holds more than just the last output but either several or intermediate...

+1 It would also be great if the solvers would return the integration up to the point where an error was thrown.

@FedericoV: this would definitely be cool to have in ODE.jl, if you ever find the time to look into it again. @ChrisRackauckas: as you probably know, Sundials can do this....

@FedericoV yes, you're right! I guess I was just referring to sensitivity analysis.

Yes, I agree, eg #72 uses in-place. I think this can be done without disturbing the high level API.

Another reference is [Hairer, Wanner & Lubich, 2002](http://link.springer.com/book/10.1007/978-3-662-05018-7), chapter VIII.