High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
112 Stars
Updated Last
1 Year Ago
Started In
August 2020


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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. Use the in-development documentation for the version of the documentation which contains the unreleased features.

High Level Examples

using NonlinearSolve, StaticArrays

f(u, p) = u .* u .- 2
u0 = @SVector[1.0, 1.0]
probN = NonlinearProblem(f, u0)
solver = solve(probN, NewtonRaphson(), abstol = 1e-9)

## Bracketing Methods

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

v1.0 Breaking Release Highlights!

v1.0 has been released for NonlinearSolve.jl, making it a decentralized solver library akin to DifferentialEquations.jl. For simple implementations of nonlinear solvers, you can now use SimpleNonlinearSolve.jl. Falsi, Bisection, and NewtonRaphson implementations designed for scalar and static vector inputs have all moved to the lower dependency version. NonlinearSolve.jl is thus designed for the larger scale more complex implementations, with NewtonRaphson now sporting support for LinearSolve.jl and soon SparseDiffTools.jl to allow for preconditioned Newton-Krylov and exploitation of sparsity. The two pieces will continue to grow in this direction, with NonlinearSolve.jl gaining more and more wrapped solver libraries and support for more complex methods, while SimpleNonlinearSolve.jl will keep a lower dependency version with implementations for small scale problems that do not need all of the extra tooling.

Additionally, NonlinearProblem was split into NonlinearProblem and IntervalNonlinearProblem, i.e. the bracketing versions now have their own problem definition, rather than using a Tuple for u0 in a NonlinearProblem. This helps for finding problem-algorithm pairing errors at type time and overall improves the documentation / makes the roles more clear.