fix: typos

Author: avik-pal

lib/NonlinearSolveBase/src/autodiff.jl

@@ -1,5 +1,5 @@
 # Here we determine the preferred AD backend. We have a predefined list of ADs and then
-# we select the first one that is avialable and would work with the problem.
+# we select the first one that is available and would work with the problem.
 
 # Ordering is important here. We want to select the first one that is compatible with the
 # problem.
@@ -29,7 +29,7 @@ function select_forward_mode_autodiff(
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_forward_mode_autodiff(prob, nothing; warn_check_mode)
         @warn "The chosen AD backend `$(ad)` does not support the chosen problem. This \
-               could be because the backend package for the choosen AD isn't loaded. After \
+               could be because the backend package for the chosen AD isn't loaded. After \
                running autodiff selection detected `$(adₙ)` as a potential forward mode \
                backend."
         return adₙ
@@ -59,7 +59,7 @@ function select_reverse_mode_autodiff(
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_reverse_mode_autodiff(prob, nothing; warn_check_mode)
         @warn "The chosen AD backend `$(ad)` does not support the chosen problem. This \
-               could be because the backend package for the choosen AD isn't loaded. After \
+               could be because the backend package for the chosen AD isn't loaded. After \
                running autodiff selection detected `$(adₙ)` as a potential reverse mode \
                backend."
         return adₙ
@@ -80,7 +80,7 @@ function select_jacobian_autodiff(prob::AbstractNonlinearProblem, ad::AbstractAD
     if incompatible_backend_and_problem(prob, ad)
         adₙ = select_jacobian_autodiff(prob, nothing)
         @warn "The chosen AD backend `$(ad)` does not support the chosen problem. This \
-               could be because the backend package for the choosen AD isn't loaded. After \
+               could be because the backend package for the chosen AD isn't loaded. After \
                running autodiff selection detected `$(adₙ)` as a potential jacobian \
                backend."
         return adₙ