diff --git a/lib/OrdinaryDiffEqDifferentiation/src/derivative_utils.jl b/lib/OrdinaryDiffEqDifferentiation/src/derivative_utils.jl
index a5babda26f..da627a55f8 100644
--- a/lib/OrdinaryDiffEqDifferentiation/src/derivative_utils.jl
+++ b/lib/OrdinaryDiffEqDifferentiation/src/derivative_utils.jl
@@ -335,7 +335,7 @@ function Base.convert(::Type{AbstractMatrix}, W::WOperator{IIP}) where {IIP}
     else
         # Non-allocating already updated
         #_W = W._concrete_form
-        #jacobian2W!(_W, W.mass_matrix, W.gamma, W.J, W.transform)
+        #jacobian2W!(_W, W.mass_matrix, W.gamma, convert(AbstractMatrix, W.J), W.transform)
     end
     return W._concrete_form
 end
@@ -455,7 +455,11 @@ function do_newJW(integrator, alg, nlsolver, repeat_step)::NTuple{2, Bool}
     integrator.iter <= 1 && return true, true # at least one JW eval at the start
     repeat_step && return false, false
     islin, _ = islinearfunction(integrator)
-    islin && return false, false # no further JW eval when it's linear
+    if islin
+        # no further J eval when it's linear
+        # W eval needed if not adaptive
+        return false, !integrator.opts.adaptive
+    end
     !integrator.opts.adaptive && return true, true # Not adaptive will always refactorize
     errorfail = integrator.EEst > one(integrator.EEst)
     if alg isa DAEAlgorithm