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Update NonlinearSystemSolvers.md
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ChrisRackauckas authored Mar 22, 2023
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Expand Up @@ -7,19 +7,23 @@ Solves for ``f(u)=0`` in the problem defined by `prob` using the algorithm

## Recommended Methods

`TrustRegion` is a good choice for most problems. For large
`NewtonRaphson` is a good choice for most problems. For large
systems, it can make use of sparsity patterns for sparse automatic differentiation
and sparse linear solving of very large systems. That said, as a classic Newton
method, its stability region can be smaller than other methods. Meanwhile,
`SimpleNewtonRaphson` and `SimpleTrustRegion` are implementations which are specialized for
small equations. They are non-allocating on static arrays and thus really well-optimized
`SimpleNewtonRaphson` is an implementation which is specialized for
small equations. It is non-allocating on static arrays and thus really well-optimized
for small systems, thus usually outperforming the other methods when such types are
used for `u0`. `DynamicSS` can be a good choice for high stability.

For a system which is very non-stiff (i.e., the condition number of the Jacobian
is small, or the eigenvalues of the Jacobian are within a few orders of magnitude),
then `NLSolveJL`'s `:anderson` can be a good choice.

!!! note

`TrustRegion` and `SimpleTrustRegion` are still in development.

## Full List of Methods

!!! note
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