https://github.com/SciML/NonlinearSolve.jl

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
https://github.com/SciML/NonlinearSolve.jl

bracketing deep-equilibrium-models differential-equations equilibrium factorization high-performance-computing julia newton-krylov newton-method newton-raphson nonlinear-equations scientific-machine-learning sciml sparse-matrices sparse-matrix steady-state

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

• Host: GitHub
• URL: https://github.com/SciML/NonlinearSolve.jl
• Owner: SciML
• License: mit
• Created: 2020-08-30T10:54:01.000Z (about 4 years ago)
• Default Branch: master
• Last Pushed: 2024-07-17T16:25:23.000Z (4 months ago)
• Last Synced: 2024-07-22T22:44:20.995Z (4 months ago)
• Topics: bracketing, deep-equilibrium-models, differential-equations, equilibrium, factorization, high-performance-computing, julia, newton-krylov, newton-method, newton-raphson, nonlinear-equations, scientific-machine-learning, sciml, sparse-matrices, sparse-matrix, steady-state
• Language: Julia
• Homepage: https://docs.sciml.ai/NonlinearSolve/stable/
• Size: 19.8 MB
• Stars: 220
• Watchers: 13
• Forks: 39
• Open Issues: 38
• Metadata Files:
  • Readme: README.md
  • License: LICENSE
  • Citation: CITATION.cff

Awesome Lists containing this project

• awesome-sciml - SciML/NonlinearSolve.jl: High-performance and differentiation-enabled nonlinear solvers

README

        
# NonlinearSolve.jl

[![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)

[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/NonlinearSolve/stable/)

[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.10397607.svg)](https://doi.org/10.5281/zenodo.10397607)

[![codecov](https://codecov.io/gh/SciML/NonlinearSolve.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/SciML/NonlinearSolve.jl)

[![Build Status](https://github.com/SciML/NonlinearSolve.jl/workflows/CI/badge.svg)](https://github.com/SciML/NonlinearSolve.jl/actions?query=workflow%3ACI)

[![Build status](https://badge.buildkite.com/413dc8df7d555cc14c262aba066503a9e7a42023f9cfb75a55.svg?branch=master)](https://buildkite.com/julialang/nonlinearsolve-dot-jl)

[![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor%27s%20Guide-blueviolet)](https://github.com/SciML/ColPrac)

[![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)

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 and others},

  journal={arXiv preprint arXiv:2403.16341},

  year={2024}

}

```