Partial revert of PR SciML#1188: Copy cache for SplitFunction in promote_f

This partially reverts PR SciML#1188 to fix convergence issues in OrdinaryDiffEq.jl split ODE methods. Instead of returning the SplitFunction unchanged (which can leave uninitialized cache memory), we now copy the cache to ensure proper initialization.

The change:
- Returns the original function if there's no cache
- If there is a cache, remakes the function with a copy of the cache
- This ensures the cache is properly initialized without replacing LazyBufferCache with zero(u0)

This fixes the convergence test failures in OrdinaryDiffEq.jl (AlgConvergence_III and others) while preserving the intent of PR SciML#1188 to not replace LazyBufferCache unnecessarily.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

src/solve.jl

@@ -863,7 +863,14 @@ end
 
 hasdualpromote(u0, t) = true
 
-promote_f(f::SplitFunction, ::Val{specialize}, u0, p, t) where {specialize} = f
+function promote_f(f::SplitFunction, ::Val{specialize}, u0, p, t) where {specialize}
+    if isnothing(f._func_cache)
+        f
+    else
+        # Copy the cache to ensure it's properly initialized
+        remake(f, _func_cache = copy(f._func_cache))
+    end
+end
 prepare_alg(alg, u0, p, f) = alg
 
 function get_concrete_tspan(prob, isadapt, kwargs, p)