MOLFiniteDifference: NonlinearProblem

[ChrisRackauckas]

#250 (comment)

Basically, I think it needs to be like MOLFiniteDifference(dx,odedim = t), i.e., you need to choose which dimension to not discretize. If you discretize all dimensions, then you get a NonlinearProblem, i.e. a nonlinear system that is implicit in all directions. This would allow us to handle things in a more principled way rather than relying on t.

[ChrisRackauckas]

#349 fixes the preferred dimension by making the choice required. However, we should have a ImplicitFiniteDifference discretization for handling the case of NonlinearProblem.

[akashkgarg]

Just so I understand the intent, is the idea here to generalize symbolic_discretize so that it will discretize over all independent variables and not assume the presence of "time"? Then return a NonlinearSystem, which is then used to createa a NonlinearProblem after structural simplification?

[ChrisRackauckas]

Yes exactly.

[ChrisRackauckas]

This was completed.