add explicit case back in for comparison. fixed a potential initializ…

…ation issue

src/unsteady.jl

@@ -54,10 +54,37 @@ Make adjoint more efficienet for time-marching analysis.
 """
 explicit_unsteady(solve, initialize, perform_step, x, p=(); cache=nothing) = _explicit_unsteady(solve, initialize, perform_step, x, p, cache)
 
-# If no AD, or Forward AD, just solve normally.
+# If no AD just solve normally.
 _explicit_unsteady(solve, initialize, perform_step, x, p, cache) = solve(x, p)
 
 
+# Overloaded for ForwardDiff
+function _explicit_unsteady(solve, initialize, perform_step, x::AbstractVector{<:ForwardDiff.Dual{T}}, p, cache) where {T}
+
+    # evaluate solver
+    xv = fd_value(x)
+    yv, tv = solve(xv, p)  # TODO: if we have explicit (not adaptive) time steps we can skip this
+
+    # get solution dimensions
+    ny, nt = size(yv)
+
+    # initialize output and caches
+    yd = similar(x, ny, nt)
+
+    # --- Initial Time Step --- #
+    # solve for Jacobian-vector products
+    @views yd[:, 1] = initialize(tv[1], x, p)
+
+    # --- Additional Time Steps ---
+    perform_step! = _make_perform_step_inplace(perform_step)
+    @views for i = 2:nt
+        perform_step!(yd[:, i], yd[:, i-1], tv[i], tv[i-1], x, p)
+    end
+
+    return yd, tv
+end
+
+
 # ReverseDiff cases
 _explicit_unsteady(solve, initialize, perform_step, x::ReverseDiff.TrackedArray, p, cache) = _explicit_unsteady_reverse_wrapper(solve, initialize, perform_step, x, p, cache)
 _explicit_unsteady(solve, initialize, perform_step, x::AbstractVector{<:ReverseDiff.TrackedReal}, p, cache) = _explicit_unsteady_reverse_wrapper(solve, initialize, perform_step, x, p, cache)
@@ -108,11 +135,11 @@ function explicit_unsteady_cache(initialize, perform_step, x, p=(); compile=fals
     y0 = initialize([1.0], x, p)
 
     # allocate inputs
-    gyprev = similar(y0)
+    gyprev = ones(length(y0))
     gt = ones(1)
     gtprev = zeros(1)
-    gx = similar(x)
-    gλ = similar(y0)
+    gx = ones(length(x))
+    gλ = ones(length(y0))
 
     # if out of place - make in-place
     perform_step! = _make_perform_step_inplace(perform_step)