DDEProblemLibrary: fix sign error in RADAR5 Oregonator (u1 equation)

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas.

What changed and why

prob_dde_RADAR5_oregonator computes a = -k₁*A*u[2] - k₂*u[1]*v once and uses it in both components, so du[1] gets -k₁ A u₂ where RADAR5 has +k₁ A u₂. The RADAR5 driver (RADAR5-V2.1/OREGONATOR/dr-oregon.f, from http://www.unige.ch/~hairer/radar5-v2.1.tar) has:

F(1)=  kM1*A*Y(2) - kM2*Y(1)*Y2L1 + kM3*B*Y(1)-2.D0*kM4*Y(1)**2
F(2)= -kM1*A*Y(2) - kM2*Y(1)*Y2L1 + fr*kM3*B*Y(1)

With the wrong sign, u₁ decays to 0 and the solution stays flat at u₂ ≈ 1e-5 on [0, 100.5], so the SciMLBenchmarks StiffDDE/Oregonator_wpd page compares solvers on a trivial solution. This PR fixes the RHS and the docstring, adds a Core test comparing the RHS to the RADAR5 FCN, and bumps DDEProblemLibrary to 0.1.10.

Verification

Before/after solution with MethodOfSteps(Rodas5P()), reltol = 1e-9, abstol = 1e-18 (DelayDiffEq 6.4.0, Julia 1.11.9), u₂ sampled at t = 0:5:100:

library (current): retcode=Success nsteps=85    u1 range=(-5.18e-11, 1.0e-10) u2 range=(9.9998e-6, 1.0e-5)
  u2: [1.0e-5, 1.0e-5, 1.0e-5, ... 1.0e-5]
RADAR5 RHS (this PR): retcode=Success nsteps=19662 u1 range=(5.06e-11, 1.86e-7) u2 range=(2.83e-7, 1.0e-5)
  u2: [1.0e-5, 4.48e-6, 2.0e-6, 8.96e-7, 4.01e-7, 3.53e-7, 3.11e-7, 3.02e-7, 4.7e-7, 4.13e-7, 3.63e-7, 3.2e-7, 3.09e-7, 4.84e-7, 4.26e-7, 3.74e-7, 3.29e-7, 2.94e-7, 6.21e-7, 4.39e-7, 3.86e-7]

New test fails without the fix (GROUP=Core, lib/DDEProblemLibrary, Julia 1.11):

RADAR5 Oregonator right-hand side: Test Failed at .../lib/DDEProblemLibrary/test/radar5.jl:16
  Expression: ≈(du, expected, rtol = 1.0e-12)
   Evaluated: [-8.69948e-5, -8.69628e-5] ≈ [-8.58692e-5, -8.69628e-5] (rtol=1.0e-12)
ERROR: LoadError: Some tests did not pass: 0 passed, 1 failed, 0 errored, 0 broken.

and passes with it:

Test Summary: | Pass  Total  Time
Load Tests    |    1      1  0.1s
Test Summary: | Pass  Total  Time
RADAR5        |    1      1  4.0s
     Testing DDEProblemLibrary tests passed

GROUP=QA: Aqua | 20 20, passed. Runic --check and typos clean on changed files.

Not verified

Julia lts/pre not run locally (only 1.11). The problem's solution changes, so any downstream results that use prob_dde_RADAR5_oregonator (SciMLBenchmarks StiffDDE/Oregonator_wpd) change with this release.

🤖 Generated with Claude Code (model: claude-opus-5-5[1m])

https://claude.ai/code/session_01Vrsu4PESdABpNaxYiTBVfd