diff --git a/src/MATLABDiffEq.jl b/src/MATLABDiffEq.jl
index a70a724..12c0c96 100644
--- a/src/MATLABDiffEq.jl
+++ b/src/MATLABDiffEq.jl
@@ -6,12 +6,15 @@ using MATLAB, ModelingToolkit
 using PrecompileTools
 
 # MATLAB only supports Float64 arrays. Check if a type is MATLAB-compatible.
+# Note: We specifically accept standard Julia integer types that MATLAB can convert,
+# but NOT BigInt since MATLAB doesn't support arbitrary precision integers.
 _is_matlab_compatible_eltype(::Type{Float64}) = true
-_is_matlab_compatible_eltype(::Type{<:Integer}) = true  # MATLAB can convert integers
+_is_matlab_compatible_eltype(::Type{<:Union{Int8, Int16, Int32, Int64, Int128}}) = true
+_is_matlab_compatible_eltype(::Type{<:Union{UInt8, UInt16, UInt32, UInt64, UInt128}}) = true
 _is_matlab_compatible_eltype(::Type{<:Complex{Float64}}) = true
 _is_matlab_compatible_eltype(::Type) = false
 
-function _check_matlab_compatible(u0, tspan)
+function _check_matlab_compatible(u0, tspan)::Nothing
     T = eltype(u0)
     if !_is_matlab_compatible_eltype(T)
         throw(
@@ -207,8 +210,10 @@ end
         # Precompile type compatibility checks
         _ = _is_matlab_compatible_eltype(Float64)
         _ = _is_matlab_compatible_eltype(Int64)
+        _ = _is_matlab_compatible_eltype(UInt64)
         _ = _is_matlab_compatible_eltype(Complex{Float64})
         _ = _is_matlab_compatible_eltype(BigFloat)
+        _ = _is_matlab_compatible_eltype(BigInt)
         _ = _check_matlab_compatible([1.0, 2.0], (0.0, 1.0))
         _ = _check_matlab_compatible(1.0, (0.0, 1.0))
     end
diff --git a/test/jet_tests.jl b/test/jet_tests.jl
index 1770416..11d9645 100644
--- a/test/jet_tests.jl
+++ b/test/jet_tests.jl
@@ -106,4 +106,54 @@ end
         @test isconcretetype(ode15s_test)
         @test isconcretetype(ode15i_test)
     end
+
+    @testset "Type compatibility functions" begin
+        # Test the type compatibility check functions
+        # These mirror the actual module implementations
+        # Note: BigInt is NOT accepted because MATLAB doesn't support arbitrary precision
+
+        _is_matlab_compatible_eltype_test(::Type{Float64})::Bool = true
+        _is_matlab_compatible_eltype_test(::Type{<:Union{Int8, Int16, Int32, Int64, Int128}})::Bool = true
+        _is_matlab_compatible_eltype_test(::Type{<:Union{UInt8, UInt16, UInt32, UInt64, UInt128}})::Bool = true
+        _is_matlab_compatible_eltype_test(::Type{<:Complex{Float64}})::Bool = true
+        _is_matlab_compatible_eltype_test(::Type)::Bool = false
+
+        # Test return types are Bool
+        @test _is_matlab_compatible_eltype_test(Float64) === true
+        @test _is_matlab_compatible_eltype_test(Int64) === true
+        @test _is_matlab_compatible_eltype_test(UInt64) === true
+        @test _is_matlab_compatible_eltype_test(Complex{Float64}) === true
+        @test _is_matlab_compatible_eltype_test(BigFloat) === false
+        @test _is_matlab_compatible_eltype_test(BigInt) === false
+        @test _is_matlab_compatible_eltype_test(Float32) === false
+
+        # JET @test_opt analysis for type stability
+        if HAS_JET
+            @testset "JET @test_opt type stability" begin
+                # Test type stability of _is_matlab_compatible_eltype
+                @test_opt _is_matlab_compatible_eltype_test(Float64)
+                @test_opt _is_matlab_compatible_eltype_test(Int64)
+                @test_opt _is_matlab_compatible_eltype_test(BigFloat)
+            end
+        end
+    end
+
+    @testset "Return type inference" begin
+        # Test that return types can be inferred correctly
+        function buildDEStats_test2(solverstats::Dict{String, <:Any})::DiffEqBase.Stats
+            destats = DiffEqBase.Stats(0)
+            destats.nf = Int(get(solverstats, "nfevals", 0))
+            destats.nreject = Int(get(solverstats, "nfailed", 0))
+            destats.naccept = Int(get(solverstats, "nsteps", 0))
+            destats.nsolve = Int(get(solverstats, "nsolves", 0))
+            destats.njacs = Int(get(solverstats, "npds", 0))
+            destats.nw = Int(get(solverstats, "ndecomps", 0))
+            destats
+        end
+
+        # Verify return type is inferred as concrete
+        return_types = Base.return_types(buildDEStats_test2, (Dict{String, Any},))
+        @test length(return_types) == 1
+        @test return_types[1] == DiffEqBase.Stats
+    end
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 51c0a3b..53cd636 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -3,6 +3,9 @@ using DiffEqBase, MATLABDiffEq, ParameterizedFunctions, Test
 # Interface tests - these test type validation without needing MATLAB runtime
 include("interface_tests.jl")
 
+# JET static analysis tests - these also run without MATLAB
+include("jet_tests.jl")
+
 # The following tests require MATLAB runtime to be available
 # They test the actual ODE solving functionality