fix typos

docs/src/solvers/NonlinearSystemSolvers.md

@@ -10,7 +10,7 @@ Solves for ``f(u)=0`` in the problem defined by `prob` using the algorithm
 The default method `FastShortcutNonlinearPolyalg` is a good choice for most
 problems. It is a polyalgorithm that attempts to use a fast algorithm
 (Klement, Broyden) and if that fails it falls back to a more robust
-algorithm (`NewtonRaphson`) before falling back the most robust varient of
+algorithm (`NewtonRaphson`) before falling back the most robust variant of
 `TrustRegion`. For basic problems this will be very fast, for harder problems
 it will make sure to work.
 

docs/src/tutorials/getting_started.md

@@ -11,13 +11,13 @@ There are three types of nonlinear systems:
 
  1. The "standard nonlinear system", i.e. the `NonlinearProblem`. This is a
     system of equations with an initial condition where you want to satisfy
-    all equations simultaniously.
+    all equations simultaneously.
  2. The "interval rootfinding problem", i.e. the `IntervalNonlinearProblem`.
     This is the case where you're given an interval `[a,b]` and need to find
     where `f(u) = 0` for `u` inside the bounds.
  3. The "steady state problem", i.e. find the `u` such that `u' = f(u) = 0`.
     While related to (1), it's not entirely the same because there's a uniquely
-    defined privledged root.
+    defined privileged root.
  4. The nonlinear least squares problem, which is an overconstrained nonlinear
     system (i.e. more equations than states) which might not be satisfiable, i.e.
     there may be no `u` such that `f(u) = 0`, and thus we find the `u` which
@@ -77,7 +77,7 @@ There are multiple return codes which can mean the solve was successful, and thu
 general command `SciMLBase.successful_retcode` to check whether the solution process exited as
 intended:
 
-```@exmaple
+```@example
 SciMLBase.successful_retcode(sol)
 ```
 

src/dfsane.jl

@@ -6,8 +6,8 @@
 
 A low-overhead and allocation-free implementation of the df-sane method for solving large-scale nonlinear
 systems of equations. For in depth information about all the parameters and the algorithm,
-see the paper: [W LaCruz, JM Martinez, and M Raydan (2006), Spectral residual mathod without
-gradient information for solving large-scale nonlinear systems of equations, Mathematics of
+see the paper: [W LaCruz, JM Martinez, and M Raydan (2006), Spectral Residual Method without
+Gradient Information for Solving Large-Scale Nonlinear Systems of Equations, Mathematics of
 Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_Spectral_Residual_Method_without_Gradient_Information_for_Solving_Large-Scale_Nonlinear_Systems_of_Equations)
 
 ### Keyword Arguments

src/trustRegion.jl

@@ -600,7 +600,7 @@ function dogleg!(cache::TrustRegionCache{true})
         return
     end
 
-    # Take the intersection of dogled with trust region if Cauchy point lies inside the trust region
+    # Take the intersection of dogleg with trust region if Cauchy point lies inside the trust region
     @. u_cauchy = -(d_cauchy / l_grad) * cache.g # compute Cauchy point
     @. u_tmp = u_gauss_newton - u_cauchy # calf of the dogleg -- use u_tmp to avoid allocation
 
@@ -630,7 +630,7 @@ function dogleg!(cache::TrustRegionCache{false})
         return
     end
 
-    # Take the intersection of dogled with trust region if Cauchy point lies inside the trust region
+    # Take the intersection of dogleg with trust region if Cauchy point lies inside the trust region
     u_cauchy = -(d_cauchy / l_grad) * cache.g # compute Cauchy point
     u_tmp = u_gauss_newton - u_cauchy # calf of the dogleg
     a = dot(u_tmp, u_tmp)