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.
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, ITP())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.