fix(Rosenbrock): strip_cache override and Hermite first-derivative interpolant

- Add OrdinaryDiffEqCore.strip_cache(::RosenbrockCache) to fix InterfaceI
  failures: generic version passes all-Nothing args but concrete-typed fields
  (dense, dtC, dtd, ks, interp_order) reject Nothing
- Add interp_order==-1 branch to all 4 Val{1} interpolant methods to fix
  Regression_I BoundsError: empty-H Hermite uses k[1]=f₀,k[2]=f₁ but old
  else-branch accessed k[3]

Author: Harsh Singh

lib/OrdinaryDiffEqRosenbrock/src/interp_func.jl

@@ -27,3 +27,30 @@ function SciMLBase.interp_summary(
         "specialized 4th (Rodas6P = 5th) order \"free\" stiffness-aware interpolation" :
         "1st order linear"
 end
+
+# strip_cache for RosenbrockCache: the generic OrdinaryDiffEqCore version passes
+# all-Nothing args, but several fields (dense, dtC, dtd, ks, interp_order) have
+# concrete types that don't accept Nothing.  Provide a custom override that clears
+# only the interpolation-related fields to zero-length arrays / nothing.
+function OrdinaryDiffEqCore.strip_cache(cache::RosenbrockCache)
+    return RosenbrockCache(
+        cache.u, cache.uprev,
+        similar(cache.dense, 0),     # dense::Vector{rateType} — must not be Nothing
+        cache.du, cache.du1, cache.du2,
+        similar(cache.dtC, 0, 0),    # dtC::Matrix{tabType}   — must not be Nothing
+        similar(cache.dtd, 0),       # dtd::Vector{tabType}   — must not be Nothing
+        similar(cache.ks, 0),        # ks::Vector{rateType}   — must not be Nothing
+        cache.fsalfirst, cache.fsallast, cache.dT,
+        cache.J, cache.W,
+        cache.tmp, cache.atmp, cache.weight,
+        cache.tab,
+        nothing,                     # tf
+        nothing,                     # uf
+        cache.linsolve_tmp, cache.linsolve,
+        nothing,                     # jac_config
+        nothing,                     # grad_config
+        cache.reltol, cache.alg,
+        cache.step_limiter!, cache.stage_limiter!,
+        cache.interp_order           # interp_order::Int — must not be Nothing
+    )
+end

lib/OrdinaryDiffEqRosenbrock/src/rosenbrock_interpolants.jl

@@ -145,7 +145,13 @@ end
         },
         idxs::Nothing, T::Type{Val{1}}, differential_vars
     )
-    if !hasproperty(cache, :interp_order) || cache.interp_order == 2
+    if hasproperty(cache, :interp_order) && cache.interp_order == -1
+        # Hermite interpolation: k[1]=f₀, k[2]=f₁
+        # dH/dt = 6Θ(1-Θ)(y₁-y₀)/dt + f₀(3Θ²-4Θ+1) + f₁(3Θ²-2Θ)
+        @.. 6 * Θ * (1 - Θ) * (y₁ - y₀) / dt +
+            k[1] * (3 * Θ^2 - 4 * Θ + 1) +
+            k[2] * (3 * Θ^2 - 2 * Θ)
+    elseif !hasproperty(cache, :interp_order) || cache.interp_order == 2
         @.. (k[1] + Θ * (-2 * k[1] + 2 * k[2] - 3 * k[2] * Θ) - y₀ + y₁) / dt
     elseif cache.interp_order == 4
         @.. (
@@ -177,7 +183,12 @@ end
         },
         idxs, T::Type{Val{1}}, differential_vars
     )
-    if !hasproperty(cache, :interp_order) || cache.interp_order == 2
+    if hasproperty(cache, :interp_order) && cache.interp_order == -1
+        # Hermite interpolation: k[1]=f₀, k[2]=f₁
+        @views @.. 6 * Θ * (1 - Θ) * (y₁[idxs] - y₀[idxs]) / dt +
+            k[1][idxs] * (3 * Θ^2 - 4 * Θ + 1) +
+            k[2][idxs] * (3 * Θ^2 - 2 * Θ)
+    elseif !hasproperty(cache, :interp_order) || cache.interp_order == 2
         @views @.. (
             k[1][idxs] +
                 Θ * (-2 * k[1][idxs] + 2 * k[2][idxs] - 3 * k[2][idxs] * Θ) -
@@ -215,7 +226,12 @@ end
         },
         idxs::Nothing, T::Type{Val{1}}, differential_vars
     )
-    if !hasproperty(cache, :interp_order) || cache.interp_order == 2
+    if hasproperty(cache, :interp_order) && cache.interp_order == -1
+        # Hermite interpolation: k[1]=f₀, k[2]=f₁
+        @.. out = 6 * Θ * (1 - Θ) * (y₁ - y₀) / dt +
+            k[1] * (3 * Θ^2 - 4 * Θ + 1) +
+            k[2] * (3 * Θ^2 - 2 * Θ)
+    elseif !hasproperty(cache, :interp_order) || cache.interp_order == 2
         @.. out = (k[1] + Θ * (-2 * k[1] + 2 * k[2] - 3 * k[2] * Θ) - y₀ + y₁) / dt
     elseif cache.interp_order == 4
         @.. out = (
@@ -249,7 +265,12 @@ end
         },
         idxs, T::Type{Val{1}}, differential_vars
     )
-    if !hasproperty(cache, :interp_order) || cache.interp_order == 2
+    if hasproperty(cache, :interp_order) && cache.interp_order == -1
+        # Hermite interpolation: k[1]=f₀, k[2]=f₁
+        @views @.. out = 6 * Θ * (1 - Θ) * (y₁[idxs] - y₀[idxs]) / dt +
+            k[1][idxs] * (3 * Θ^2 - 4 * Θ + 1) +
+            k[2][idxs] * (3 * Θ^2 - 2 * Θ)
+    elseif !hasproperty(cache, :interp_order) || cache.interp_order == 2
         @views @.. out = (
             k[1][idxs] +
                 Θ *