https://github.com/fgittins/nonlinearsolve.jl

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

https://github.com/fgittins/nonlinearsolve.jl

Repository

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

https://github.com/fgittins/NonlinearSolve.jl/blob/master/

# NonlinearSolve.jl

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Fast implementations of root finding algorithms in Julia that satisfy the SciML common interface.

For information on using the package,
[see the stable documentation](https://docs.sciml.ai/NonlinearSolve/stable/). Use the
[in-development documentation](https://docs.sciml.ai/NonlinearSolve/dev/) for the version of
the documentation which contains the unreleased features.

## High Level Examples

```julia
using NonlinearSolve, StaticArrays

f(u, p) = u .* u .- 2
u0 = @SVector[1.0, 1.0]
prob = NonlinearProblem(f, u0)
solver = solve(prob)

## Bracketing Methods

f(u, p) = u .* u .- 2.0
u0 = (1.0, 2.0) # brackets
prob = IntervalNonlinearProblem(f, u0)
sol = solve(prob)
```

## Citation

If you found this library to be useful in academic work, then please cite:

```bibtex
@article{pal2024nonlinearsolve,
  title={NonlinearSolve. jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia},
  author={Pal, Avik and Holtorf, Flemming and Larsson, Axel and Loman, Torkel and Schaefer, Frank and Qu, Qingyu and Edelman, Alan and Rackauckas, Chris},
  journal={arXiv preprint arXiv:2403.16341},
  year={2024}
}
```

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