Add Float64 convergence tests for DPRKN methods

Add regression tests to ensure CompiledFloats coefficients match the expected
convergence order for DPRKN4, DPRKN5, DPRKN6, DPRKN6FM, and DPRKN8.

These tests specifically target the Float64 code path (CompiledFloats) which
was the source of the DPRKN5 bug fixed in this PR. The existing BigFloat tests
only exercise the rational coefficient path.

Note: DPRKN12 is too accurate for Float64 testing (hits machine precision even
at dt=1.0), so it's only tested with BigFloat.

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Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

Author: ChrisRackauckas

lib/OrdinaryDiffEqRKN/test/nystrom_convergence_tests.jl

@@ -47,6 +47,36 @@ sim = test_convergence(dts, prob_big, ERKN7(), dense_errors = true)
 @test sim.𝒪est[:l2]≈7 rtol=1e-1
 @test sim.𝒪est[:L2]≈4 rtol=1e-1
 
+# Float64 convergence tests for DPRKN methods
+# These tests ensure the CompiledFloats coefficients match the rational coefficients
+# (Regression test for https://github.com/SciML/OrdinaryDiffEq.jl/issues/1938)
+@testset "Float64 DPRKN convergence" begin
+    # Use longer integration time to keep errors above machine precision
+    prob_f64 = DynamicalODEProblem(ff_harmonic, ones(2), fill(0.0, 2), (0.0, 20.0))
+    dts_f64 = 1.0 ./ 2.0 .^ (2:5)
+
+    sim = test_convergence(dts_f64, prob_f64, DPRKN4())
+    @test sim.𝒪est[:l2]≈4 rtol=1e-1
+
+    sim = test_convergence(dts_f64, prob_f64, DPRKN5())
+    @test sim.𝒪est[:l2]≈5 rtol=1e-1
+
+    sim = test_convergence(dts_f64, prob_f64, DPRKN6())
+    @test sim.𝒪est[:l2]≈6 rtol=1e-1
+
+    sim = test_convergence(dts_f64, prob_f64, DPRKN6FM())
+    @test sim.𝒪est[:l2]≈6 rtol=1e-1
+
+    # DPRKN8 needs larger timesteps and longer integration to avoid hitting machine precision
+    prob_f64_long = DynamicalODEProblem(ff_harmonic, ones(2), fill(0.0, 2), (0.0, 50.0))
+    dts_f64_large = [1.0, 0.5, 0.25, 0.125]
+    sim = test_convergence(dts_f64_large, prob_f64_long, DPRKN8())
+    @test sim.𝒪est[:l2]≈8 rtol=1e-1
+
+    # DPRKN12 is too accurate for Float64 convergence testing (hits machine precision
+    # even at dt=1.0), so we only test it with BigFloat (see tests above)
+end
+
 sol = solve(prob, Nystrom4(), dt = 1 / 1000)
 
 # Nyström method