I have a few questions:
 What is the difference in scope between NonlinearSolve.jl and NLSolvers.jl/NLsolve.jl?
 What are the pros/cons of NonlinearSolve.jl vs NLSolvers.jl/NLsolve.jl?
 Are there any plans to include the algorithms of SIAMFANLEquations.jl into either/both of NonlinearSolve.jl and NLSolvers.jl/NLsolve.jl?
 In particular, any plans to include the pseudotransient continuation solver? Or maybe there are some other versions out there?
 Are there other packages/solvers I should know about for solving large nonlinear systems?
For context, I deal with largeish (up to ~1M) systems of nonlinear ODEs of marine tracers, for which I develop AIBECS.jl to, well, simulate these tracers. AIBECS essentially provides the tooling for users to create the functions that define the system of ODEs. In SciMLâs lingo, it creates two functions of the state variable u
and the parameters p
:
F(u,p) = f(u, p, t) > the rate of change of the system
ââF(u,p) = jac(u, p, t) > the jacobian of f with respect to u
As you may notice, there is no t
dependency for my case of f
and jac
, and so most of the time, I am looking for the steadystate of these ODEs. To solve for that steadystate, I currently use my own rewrite of @ctkelleyâs MATLAB nsold.m
(which is probably not optimal, in the sense that my rewrite is not optimal, not his algorithms, to be precise! ). In other words, for a given set of parameters p
, I feed x > f(x,p,0)
and x > jac(x,p,0)
to the newton solver to find the root x
such that f(x,p,0) â 0
. Now this all works already quite well in my opinion, but Iâm always looking to improve the package, and at the time of writing, it seems I have many choices to replace my nonexpert code, among which
 NLsolve.jl by @pkofod, the most used package for solving large nonlinear systems in Julia AFAIK
 NLSolvers.jl, @pkofodâs own rewrite of NLsolve.jl, destined to replace it, but already available for those that want to live on the edge
 JuliaComputing/SciMLâs NonlinearSolve.jl, which seems to have a large overlap with NLsolve.jl/NLSolvers.jl although it seems to be targeting specifically SciML problems

SIAMFANLEquations.jl, which is @ctkelleyâs own Julia version of
nsold.m
and co, being developed in parallel to writing the corresponding book. Particularly of interest to me is the pseudotransient continuation solver, which I donât think has any equivalent in other Julia packages, and is very relevant to my research, where the initial guess may be quite far and impede the Newton algorithm convergence.
Please forgive me if I butchered your work with my ignorant definitions and assumptions, I have the utmost respect for the developers/scientists involved with these and I think these are all amazing pieces of work/software. But back to my questions: Iâm not really sure what I should be using in the future and keep asking myself these or similar questions, in my head or on slack, and I thought I should lay these down here for the experts (@pkofod, @ctkelley, @ChrisRackauckas and all the relevant SciML people, and whoever I should know about) to chime in if they want!