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Fast and simple nonlinear solvers for the SciML common interface. Newton, Broyden, Bisection, Falsi, and more rootfinders on a standard interface.

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## Checklist - [x] Appropriate tests were added - [x] Any code changes were done in a way that does not break public API - [x] All documentation related to...

## Example Usage Package is private currently ```julia using AutoBatching, SimpleNonlinearSolve function solve_nlprob(f::F, u0::AbstractVector, p::Number, alg) where {F} prob = NonlinearProblem(f, u0, p) return solve(prob, alg).u end u0 = rand(3)...

## Checklist - [x] Appropriate tests were added - [x] Any code changes were done in a way that does not break public API - [ ] All documentation related...

This is VERY Breaking * Move to NonlinearSolveBase, which is a significantly lighter version of DiffEqBase * ForwardDiff and FiniteDiff are moved into extensions, so no AD package is loaded...

First of all, thank you for this great package! When looking through the documentation of the `ITP`-Method (and the code), I noticed that the default values of the parameters are...

bug

I was playing around with JNFK for DEQs and the Nonlinear Solve implementation is a bit too complicated for those purposes - [x] Working Version - [ ] Batched Version...

https://www.semanticscholar.org/paper/A-family-of-regula-falsi-root-finding-methods-Galdino/aa7a91e09f82684f200390eb1684a1ffccc0c4f2 the api could be implemented by calling` Falsi(n::Int)` and defining `Falsi() = Falsi(default_n)`

new-algorithm

## Checklist - [ ] Appropriate tests were added - [x] Any code changes were done in a way that does not break public API - [ ] All documentation...

The warning introduced in #158 is great, however the first time I got it I had to do some googling to figure out what it meant. Specifically the wording made...

This pull request changes the compat entry for the `DifferentiationInterface` package from `0.5` to `0.5, 0.6`. This keeps the compat entries for earlier versions. Note: I have not tested your...