feat: support initialization of DiscreteProblem

[AayushSabharwal]

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

Add any other context about the problem here.

[isaacsas]

Doesn’t this need to be in SciMLBase or DiffEqBase? OrdinaryDiffEq is not a dependency of JumpProcesses so this would never get loaded for a pure JumpProblem?

[AayushSabharwal]

This is for DiscreteProblem, not JumpProblem. JumpProblem wraps another problem, and __init(jprob::JumpProblem) calls __init(jprob.prob) so the initialization there would run.

[ChrisRackauckas]

But there are methods for DiscreteProblem in for example SimpleDiffEq.jl. I think this dispatch might make sense in SciMLBase since it's not specific to any method here?

[AayushSabharwal]

It's specific to the integrator and the initializealg. Trying to solve a DiscreteProblem with FunctionMap will run into the __init defined here which will call initialize_dae! with DefaultInit as the initializealg. SimpleDiffEq doesn't hook into initialization yet, so that PR is separate.