diff --git a/docs/src/solvers/NonlinearSystemSolvers.md b/docs/src/solvers/NonlinearSystemSolvers.md index b4ef3a46d..a19a3f8a7 100644 --- a/docs/src/solvers/NonlinearSystemSolvers.md +++ b/docs/src/solvers/NonlinearSystemSolvers.md @@ -7,12 +7,12 @@ 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. @@ -20,6 +20,10 @@ 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