Merge into DifferentialEquations, NLSolve

[briochemc]

I think in the long run it will be good to somehow merge the solving functionality of this package (the solver(s) in particular) with the well maintained packages of DifferentialEquations and/or NLSolve. This would provide lots of added functionality (e.g., for #4, #5, etc.). Also this might help to provide a DSL as suggested in #18

[briochemc]

I think this MWE of using a large sparse matrix with ModelingToolkit.jl is a good place to start this!

[briochemc]

discourse post for reference: https://discourse.julialang.org/t/solving-for-the-steady-state-of-a-large-nonlinear-ode-in-sciml/50613/16

[briochemc]

Some more thoughts and notes on a hard-to-solve mode I stumbled upon. It took 75 iterations of the CTKAlg, with about 50 of them going through a two-step Armijo line search. I am thinking this might be similar to some complex dampening oscillator for which the Newton steps always overshoot the root in some directions but not others.... Anyway, it could be good to come up with a minimal example that behaves the same way (if possible). The coarser matrices help. #61 could be very useful for this. Also maybe the high-diffusivity matrices might be beneficial too.