Draft: ImplicitDiscreteSolve

[vyudu]

Requires:

• Use AbstractDiscreteProblem instead of DiscreteProblem in solve OrdinaryDiffEq.jl#2607
• fix: ImplicitDiscreteFunction IIP has 5 arguments not 6 SciMLBase.jl#937

[vyudu]

@ChrisRackauckas This is barebones but working. Any important features I'm missing here? Also should this actually go in OrdinaryDiffEq?

[ChrisRackauckas]

Can this to use SimpleNonlinearSolve.jl's Newton and make this be SimpleImplicitDiscreteSolve.jl? I think the complete version will want to use the Jacobian reuse aspect and such, so for now having a static version would be a good way to handle this.

[vyudu]

Did that refactor, just needs more tests now I think

[vyudu]

@ChrisRackauckas I think this is basically ready, initialization for problems without initializationproblems needs work but I think it's fine for the MTK purposes. How do I register it?

[vyudu]

Fixed these

[ChrisRackauckas]

Okay so this implementation finds itself in a somewhat odd spot. It's not a "Simple" alg because it's not statically compile-able, which is a property that all others have. It would need to avoid the OrdinaryDiffEqCore part. But it's not a fully complete version either? But it's a rough start towards it. I guess seeing it at this stage, how about moving this to OrdinaryDiffEq and making this be ImplicitDiscreteSolve.jl, and we can use this as a base to do the required optimizations to make the full version. We can do the SimpleImplicitDiscreteSolve.jl as a somewhat separate version for static support.

[vyudu]

I see, didn't realize I couldn't use OrdinaryDiffEqCore, will move. I'll keep this open too to keep iterating it toward a SimpleImplicitDiscreteSolve.

[ChrisRackauckas]

See for example https://github.com/SciML/SimpleDiffEq.jl/blob/master/src/rk4/looprk4.jl which is the most basic RK4 implementation. For IDS, it would just be a loop over nonlinear solve calls. With SimpleNonlinearSolve being similar, the whole thing would statically compile since no mutable structs would be in the middle.