Proposal for ODE package: multistep methods about exp

[aestriplex]

@sbinet @soypat Ok,
I'll start working on AB4 then

[sbinet]

I am quite ignorant wrt ODEs.
but as I see nobody responded yet, let me say your proposal sounds okay - to my ignorant ears.

to get the ball rolling, I'd say: try to implement the easiest of the 3 methods, together with an example (and tests).
and see what gives.

unless @kortschak @btracey @romanwerpachowski @vladimir-ch or @soypat have more insightful comments?

[soypat]

Sounds good!
I'll throw a couple related discussions your way in case you want some history on the ode package.

• mailing list discussion about API design, explains why it looks this way today.
• issue regarding jacobian calculation. diff/fd uses slices while mat types seem more appropiate for ode.
• gonum/gonum#1761 first issue on the matter