Migrate solve dispatches from DiffEqBase to NonlinearSolveBase

[jClugstor]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

[ChrisRackauckas]

not a comment, just delete.

[ChrisRackauckas]

The utilities at the top here are reused by DiffEqBase, NonlinearSolveBase, OptimizationBase (in the near future), etc. Let's move these to SciMLBase and share them across the different repos.

[ChrisRackauckas]

The allowedkwargs handling, the special error types, etc.

[jClugstor]

I thought so too, but I figured it might be nice for each to have a separate list of acceptable keywords, so if you tried to pass e.g. dtmin in to a NonlinearSolve it would give a nice error. Also the messages right now are specific to DiffEqs, they point to the DiffEq docs. I made it so that if there's a mismatch kwarg for a nonlinear solve it points to the NonlinearSolve docs.

But yeah if these are better in SciMLBase I can just put them there.

[jClugstor]

There's also a lot of small utility functions that live in DiffEqBase right now, e.g.
get_concrete_problem, extract_alg, promote_u0, anyeltypedual etc. that get used in the solve functions. I'm thinking those should also be moved to SciMLBase?

[ChrisRackauckas]

The list of acceptable kwargs, yes that one should be problem specific, that would be a nice improvement.

But the others yes.

[jClugstor]

Currently the definitions for functions like promote_u0 and anyeltypedual etc. are in different extensions in DiffEqBase. I'm thinking I should create corresponding extensions in SciMLBase for those packages and move the functions to those. But I'll keep the parts of the extensions specific to DiffEqs in the extensions in DiffEqBase.