Implicit solvers

Some docs here: https://diffeq.sciml.ai/dev/features/linear_nonlinear/

nonlinear

initialization

1. OrdinaryDiffEq.alg_cache

• Val{true} implies it operates in-place

2. Calls build_nlsolver, dispatching on AbstractNLSolverAlgorithm type: these are defined in DiffEqBase. e.g. NLNewton, which would call build_nlsolver.

   a. nf = nlsolve_f(f, alg), which extracts the implicit part if using a SplitFunction

   b. SciMLBase.islinear(f): this appears to only be true if f (or f.f1) is an AbstractDiffEqOperator that isconstant? If so, then it sets uf and jac_config to nothing, and calls linsolve(Val{:init},nf,u)

   c. build_uf: returns a SciMLBase.UJacobianWrapper, which captures the function, parameter and time, and can be called with just (dest, src) args (to make it easier to use the AD tools I assume?).

   c. build_J_W:

   - [`islinearfunction(f, alg)`]()
   

   Returns NLNewtonConstantCache object