Run PRK and PDIRK stages serially inside another threaded region

lib/OrdinaryDiffEqCore/Project.toml

@@ -1,7 +1,7 @@
 name = "OrdinaryDiffEqCore"
 uuid = "bbf590c4-e513-4bbe-9b18-05decba2e5d8"
 authors = ["ParamThakkar123 <paramthakkar864@gmail.com>"]
-version = "4.20.1"
+version = "4.20.2"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

lib/OrdinaryDiffEqCore/src/misc_utils.jl

@@ -124,6 +124,10 @@ isthreaded(::BaseThreads) = true
 isthreaded(::PolyesterThreads) = true
 
 @inline function _threaded_execute(f, ::Union{BaseThreads, Bool}, range)
+    if ccall(:jl_in_threaded_region, Cint, ()) != 0
+        foreach(f, range)
+        return nothing
+    end
     return Threads.@threads :static for i in range
         f(i)
     end

lib/OrdinaryDiffEqPRK/test/runtests.jl

@@ -23,6 +23,20 @@ end
     @test !any(Base.isexported.(Ref(OrdinaryDiffEqPRK), internal))
 end
 
+@time @safetestset "Threaded stages inside another threaded loop" begin
+    using OrdinaryDiffEqPRK, Test
+    prob_iip = ODEProblem((du, u, p, t) -> (du .= -u), [1.0, 2.0], (0.0, 1.0))
+    prob_oop = ODEProblem((u, p, t) -> -u, 1.0, (0.0, 1.0))
+    for prob in (prob_iip, prob_oop)
+        threaded = solve(prob, KuttaPRK2p5(threading = true); dt = 0.1)
+        sols = Vector{Any}(undef, 2)
+        Threads.@threads for i in 1:2
+            sols[i] = solve(prob, KuttaPRK2p5(threading = true); dt = 0.1)
+        end
+        @test all(sol -> sol.u == threaded.u, sols)
+    end
+end
+
 # Run QA tests (AllocCheck, JET, Aqua) - skip on pre-release Julia
 # Allocation tests must run before JET because JET's static analysis
 # invalidates compiled code and causes spurious runtime allocations.