There are commands like
NDSolve that have the option
Method it typically defaults to
Automatic. How can you check after the evaluation of the command which method Mathematica picked?
I think you can actually see (most of) what Mathematica is doing by using
shows the DE was evaluated using
As an aside, here's something I just learnt from Trott's Mathematica guidebook for numerics, to see all of the methods and suboptions for
Adams, BDF, IDA are multi-step methods and do not work with this approach.
I asked this question once after a presentation by Jon McLoone. His answer was that that was not possible and that Mathematica can switch methods many times if the situation asks for it. So it wouldn't be useful either. I agree that this is not completely satisfactory.