Fix wrong interpolation coefficients for Rodas3, ROS34PW3

The Rosenbrock consolidation PR (SciML#3102) added a Hermite fallback in
_ode_addsteps! for methods with empty H matrices that computed:

  k₁ = dt*f₀ - (u - uprev)
  k₂ = 2*(u - uprev) - dt*(f₀ + f₁)

But hermite_interpolant in generic_dense.jl expects k[1] = f₀ and
k[2] = f₁ (raw derivative values at endpoints). The mismatch produced
wildly wrong interpolated values at saveat points (e.g. u(0.15) = 3.97
vs correct 3.28 for the test ODE du/dt = u*p).

Remove the incorrect fallback. Methods with empty H now fall through
to the generic _ode_addsteps! which correctly stores f₀ and f₁ for
standard Hermite interpolation.

Fixes SciML/SciMLSensitivity.jl#1398 (Core2 stiff_adjoints failures).

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: ChrisRackauckas

lib/OrdinaryDiffEqRosenbrock/src/stiff_addsteps.jl

@@ -126,14 +126,10 @@ function _ode_addsteps!(
                 end
                 copyat_or_push!(k, j, kj)
             end
-        else
-            # No H matrix: compute Hermite-compatible coefficients
-            # k₁ = dt*f₀ - (y₁-y₀), k₂ = 2(y₁-y₀) - dt*(f₀+f₁)
-            f0 = f(uprev, p, t)
-            f1 = f(u, p, t + dt)
-            copyat_or_push!(k, 1, @.. dt * f0 - (u - uprev))
-            copyat_or_push!(k, 2, @.. 2 * (u - uprev) - dt * (f0 + f1))
         end
+        # Methods with empty H (Rodas3, ROS34PW3, etc.) have no dense output
+        # coefficients — fall through to the generic _ode_addsteps! which
+        # stores f₀ and f₁ for standard Hermite interpolation.
     end
     return nothing
 end
@@ -208,14 +204,10 @@ function _ode_addsteps!(
                     @.. k[j] += H[j, i] * _vec(ks[i])
                 end
             end
-        else
-            # No H matrix: compute Hermite-compatible coefficients
-            # k₁ = dt*f₀ - (y₁-y₀), k₂ = 2(y₁-y₀) - dt*(f₀+f₁)
-            f(du, uprev, p, t)
-            f(du1, u, p, t + dt)
-            copyat_or_push!(k, 1, @.. dt * du - (u - uprev))
-            copyat_or_push!(k, 2, @.. 2 * (u - uprev) - dt * (du + du1))
         end
+        # Methods with empty H (Rodas3, ROS34PW3, etc.) have no dense output
+        # coefficients — fall through to the generic _ode_addsteps! which
+        # stores f₀ and f₁ for standard Hermite interpolation.
     end
     return nothing
 end