diff --git a/docs/src/solvers/NonlinearSystemSolvers.md b/docs/src/solvers/NonlinearSystemSolvers.md index 40db41e6a..4af29e56e 100644 --- a/docs/src/solvers/NonlinearSystemSolvers.md +++ b/docs/src/solvers/NonlinearSystemSolvers.md @@ -12,7 +12,7 @@ systems, it can make use of sparsity patterns for sparse automatic differentiati 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. It is non-allocating on static arrays and thus really well-optimized +small equations. They are 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. @@ -48,16 +48,16 @@ methods excel at small problems and problems defined with static arrays. - `SimpleNewtonRaphson()`: A simplified implementation of the Newton-Raphson method. - `Broyden()`: the classic Broyden's quasi-Newton method. - `Klement()`: A quasi-Newton method due to Klement. It's supposed to be more efficient - than Broyden's method, and it seems to be in the cases that have been tried but more + than Broyden's method, and it seems to be in the cases that have been tried, but more benchmarking is required. - `SimpleTrustRegion()`: A dogleg trust-region Newton method. Improved globalizing stability for more robust fitting over basic Newton methods, though potentially with a cost. !!! note - When used with states `u` as a `Number` or `StaticArray`, these solvers are - very efficient and non-allocating. These implementations are thus well-suited for small - systems of equations. + When used with certain types for the states `u` such as a `Number` or `StaticArray`, + these solvers are very efficient and non-allocating. These implementations are thus + well-suited for small systems of equations. ### SteadyStateDiffEq.jl