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Simplify README examples to just use the default method
Fixes #209
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Diff for: README.md

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@@ -24,34 +24,13 @@ using NonlinearSolve, StaticArrays
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f(u, p) = u .* u .- 2
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u0 = @SVector[1.0, 1.0]
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probN = NonlinearProblem(f, u0)
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solver = solve(probN, NewtonRaphson(), abstol = 1e-9)
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prob = NonlinearProblem(f, u0)
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solver = solve(prob)
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## Bracketing Methods
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f(u, p) = u .* u .- 2.0
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u0 = (1.0, 2.0) # brackets
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probB = IntervalNonlinearProblem(f, u0)
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sol = solve(probB, ITP())
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prob = IntervalNonlinearProblem(f, u0)
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sol = solve(prob)
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```
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## v1.0 Breaking Release Highlights!
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v1.0 has been released for NonlinearSolve.jl, making it a decentralized solver library
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akin to DifferentialEquations.jl. For simple implementations of nonlinear solvers,
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you can now use SimpleNonlinearSolve.jl. `Falsi`, `Bisection`, and `NewtonRaphson`
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implementations designed for scalar and static vector inputs have all moved to the
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lower dependency version. NonlinearSolve.jl is thus designed for the larger scale
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more complex implementations, with `NewtonRaphson` now sporting support for
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LinearSolve.jl and soon SparseDiffTools.jl to allow for preconditioned Newton-Krylov and
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exploitation of sparsity. The two pieces will continue to grow in this direction,
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with NonlinearSolve.jl gaining more and more wrapped solver libraries and support
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for more complex methods, while SimpleNonlinearSolve.jl will keep a lower dependency
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version with implementations for small scale problems that do not need all of the
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extra tooling.
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Additionally, `NonlinearProblem` was split into `NonlinearProblem` and `IntervalNonlinearProblem`,
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i.e. the bracketing versions now have their own problem definition, rather than using
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a `Tuple` for `u0` in a `NonlinearProblem`. This helps for finding problem-algorithm
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pairing errors at type time and overall improves the documentation / makes the roles
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more clear.

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