Fix SplitODEProblem regression for non-IMEX ESDIRK methods (Kvaerno3/4/5) (#3653)

* add issplit(alg) conditions

* add issplit(alg) conditions

* add test

Author: JoshuaLampert

lib/OrdinaryDiffEqSDIRK/src/generic_imex_perform_step.jl

@@ -445,13 +445,13 @@ end
     return quote
         $setup
         if tab.explicit_first_stage
-            if integrator.f isa SplitFunction && tab.fsal && !repeat_step && !integrator.last_stepfail
+            if integrator.f isa SplitFunction && issplit(alg) && tab.fsal && !repeat_step && !integrator.last_stepfail
                 f_impl(zs[1], integrator.uprev, p, integrator.t)
                 zs[1] .*= dt
             else
                 @.. broadcast = false zs[1] = dt * integrator.fsalfirst
             end
-            if integrator.f isa SplitFunction
+            if integrator.f isa SplitFunction && issplit(alg)
                 @.. broadcast = false ks[1] = dt * integrator.fsalfirst - zs[1]
             end
             $stages_efs_true
@@ -482,7 +482,7 @@ end
 
         $adaptive
 
-        if integrator.f isa SplitFunction
+        if integrator.f isa SplitFunction && issplit(alg)
             integrator.f(integrator.fsallast, u, p, t + dt)
         elseif tab.explicit_fsallast
             integrator.f(integrator.fsallast, u, p, t + tab.fsallast_c * dt)
@@ -690,12 +690,12 @@ end
     return quote
         $setup
         if tab.explicit_first_stage
-            if integrator.f isa SplitFunction
+            if integrator.f isa SplitFunction && issplit(alg)
                 $z1 = dt * f_impl(uprev, p, t)
             else
                 $z1 = dt * integrator.fsalfirst
             end
-            if integrator.f isa SplitFunction
+            if integrator.f isa SplitFunction && issplit(alg)
                 $k1 = dt * integrator.fsalfirst - $z1
             end
             $stages_efs_true
@@ -726,7 +726,7 @@ end
 
         $adaptive
 
-        if integrator.f isa SplitFunction
+        if integrator.f isa SplitFunction && issplit(alg)
             integrator.k[1] = integrator.fsalfirst
             integrator.fsallast = integrator.f(u, p, t + dt)
             integrator.k[2] = integrator.fsallast

lib/OrdinaryDiffEqSDIRK/test/sdirk_convergence_tests.jl

@@ -183,3 +183,27 @@ end
     sim_iip = test_convergence(dts, prob_iip, ARS343())
     @test sim_iip.𝒪est[:l∞] ≈ 3 atol = testTol
 end
+
+# Regression test: Kvaerno3/4/5 with SplitODEProblem must integrate the full RHS (f1+f2),
+# not just f1. These are non-IMEX (issplit=false) methods, so f.f2 must flow through
+# fsalfirst rather than being split off into the explicit ks arrays (which have Ae=be=0).
+# f = f1 + f2 = -u + 2u = u  =>  exact solution u(t) = exp(t) * u0
+@testset "Kvaerno SplitODEProblem" begin
+    dts = 1 .// 2 .^ (8:-1:4)
+
+    f1_oop = (u, p, t) -> -u
+    f2_oop = (u, p, t) -> 2u
+    ff_oop = SplitFunction(f1_oop, f2_oop; analytic = (u0, p, t) -> exp(t) * u0)
+    prob_oop = SplitODEProblem(ff_oop, 1.0, (0.0, 1.0))
+
+    f1_iip! = (du, u, p, t) -> (du .= -u)
+    f2_iip! = (du, u, p, t) -> (du .= 2u)
+    ff_iip = SplitFunction(f1_iip!, f2_iip!; analytic = (u0, p, t) -> exp(t) .* u0)
+    prob_iip = SplitODEProblem(ff_iip, [1.0, 0.5], (0.0, 1.0))
+
+    sim_oop = test_convergence(dts, prob_oop, Kvaerno4())
+    @test sim_oop.𝒪est[:l∞] ≈ 4 atol = testTol
+
+    sim_iip = test_convergence(dts, prob_iip, Kvaerno4())
+    @test sim_iip.𝒪est[:l∞] ≈ 4 atol = testTol
+end