Fix Unitful.jl compatibility for stabilized RK methods

[ChrisRackauckas-Claude]

Summary

• Fixes issue Stabilized RK methods do not work with Unitful #2858 where stabilized RK methods (ESERK4, ESERK5, SERK2, ROCK2, ROCK4, RKC) failed when time was given as a Unitful quantity
• Root cause: The maxeig! power iteration function in rkc_utils.jl mixed quantities with rate units [u]/[t] and state units [u], causing dimensional incompatibility
• Key fixes:
  • Track whether z has rate units and multiply by dt when converting to state units
  • Use DiffEqBase.value() to strip units from dt and dtmax when computing unitless eigenvalue estimates
  • Fix quotient formula in power iteration loop to maintain constant perturbation size
  • Fix sqrt(abs(dt) * integrator.eigen_est) in perform_step to use unitless dt value

Test plan

• All 68 tests in OrdinaryDiffEqStabilizedRK pass locally
• Verified Unitful compatibility with exact test case from issue Stabilized RK methods do not work with Unitful #2858:

  using OrdinaryDiffEq, Unitful
  function lorenz!(du, u, p, t)
      du[1] = 10.0*(u[2]-u[1])
      du[2] = u[1]*(28.0-u[3]) - u[2]
      du[3] = u[1]*u[2] - (8/3)*u[3]
  end
  u0 = [1.0; 0.0; 0.0]
  tspan = (0.0u"s", 100.0u"s")
  prob = ODEProblem(lorenz!, u0, tspan)
  sol = solve(prob, ROCK4())  # Previously threw DimensionError

• CI tests

🤖 Generated with Claude Code

Co-Authored-By: Claude Opus 4.5 [email protected]