No clear winner. The survival gap is under 10 percentage points and the balanced-score gap is under 0.05, so neither SolvSRK nor the best baseline clears the win threshold. Either works — choose on cost, licensing, or integration effort. All verdicts →
Two-layer heat conduction with Stefan-Boltzmann radiative boundary conditions. Left face exchanges radiation with 500 K source, right face with 300 K ambient. The T^4 nonlinearity in the BCs makes the effective system matrix state-dependent. LRDE-ineligible. Tests boundary of LRDE applicability with realistic radiative coupling.
Incropera & DeWitt, Fundamentals of Heat Transfer, 7th ed.; Siegel & Howell, Thermal Radiation Heat Transfer, 6th ed.
Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.
def rhs(t: float, temp: np.ndarray) -> np.ndarray:
temp = np.clip(np.asarray(temp, dtype=float), 200.0, 3500.0)
d = np.zeros(n)
for i in range(n):
t_left = temp[i - 1] if i > 0 else temp[i]
t_right = temp[i + 1] if i < n - 1 else temp[i]
d[i] = alphas[i] * (t_left - 2.0 * temp[i] + t_right) / dx2
# radiative BCs: left face exchanges with 500 K source, right with ambient
q_rad_left = emissivity * stefan_boltzmann * (500.0**4 - temp[0]**4)
q_rad_right = emissivity * stefan_boltzmann * (t_ambient**4 - temp[-1]**4)
d[0] += q_rad_left / (rho_c * dx)
d[-1] += q_rad_right / (rho_c * dx)
return dCanonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.
Fingerprint
Spread: extreme
Default noise: none
Recommendation snapshot
Clean best: SolvSRK
Noisy best: SolvSRK
Coverage
14 solver arms · clean + 5 noise levels
Ranked on survival, precision, and speed
20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: Nonlinear Heat — Radiative BCs T^4 (dim=40) (nonlinear-heat-radiative-bcs-t-4-dim-40)
Governed SolvTune benchmark freeze; per-arm medians only. RHS definitions and raw trial rows are not published.
Self-reported by Resonix Labs · not independently verified
Pick an objective and a noise level to rank all arms on survival, median SCD, median nfev, and median wall time. Medians across seeds.
Objective
Best overall trade-off of survival, precision, and speed.
Noise level
| # | Solver | Survival | SCD | nfev | Wall | Score |
|---|---|---|---|---|---|---|
| 1 | SolvSRK | 100% | 11.4 | 2,032 | 66 ms | 0.890 |
| 2 | SciPy RadauSciPy | 100% | 10.6 | 1,231 | 39 ms | 0.871 |
| 3 | Tsit5external | 100% | 8.5 | 276,978 | 21.15 s | 0.822 |
| 4 | SciPy LSODASciPy | 100% | 8.4 | 1,434 | 22 ms | 0.818 |
| 5 | SciPy RK45SciPy | 100% | 8.3 | 269,024 | 5.55 s | 0.818 |
| 6 | SciPy DOP853SciPy | 100% | 8.3 | 238,970 | 4.45 s | 0.817 |
| 7 | SciPy BDFSciPy | 100% | 8.1 | 562 | 20 ms | 0.813 |
| 8 | CVODE Adamsexternal | 100% | 8.0 | 2,839 | 55 ms | 0.810 |
| 9 | CVODE BDFexternal | 100% | 8.0 | 499 | 13 ms | 0.810 |
| 10 | SciPy RK23SciPy | 100% | 7.6 | 152,012 | 2.88 s | 0.799 |
At Clean, best balanced arm is SolvSRK.
Values are medians across seeds, measured by Resonix Labs on Resonix hardware and not independently verified; nfev and wall are on reference lab hardware (indicative). Under injected noise only SolvSRK and the SciPy arms are run. How we measure accuracy → · Verification status →
SolvScout · free
This page shows one published benchmark cell. SolvScout fingerprints your ODE, compares it to the full corpus, and recommends a solver with the same survival / precision / speed ranking you see here — including when a SciPy arm wins.
SolvSRK · 30-day trial
SolvSRK is the stiffness-adaptive integrator behind the SolvSRK column in these tables. Create an account, activate a machine, and take a 30-day trial — same binary you'd ship after purchase.
Replace the access date. Pin the freeze ID and library versions when comparing against a later export. Cite it as what it is — a self-reported vendor benchmark, not an independently verified result. The note field says so; please keep it.
@misc{resonix_evidence_nonlinear_heat_radiative_bcs_t_4_dim_40_2026,
title = {Resonix Evidence Portal: Nonlinear Heat — Radiative BCs T^4 (dim=40)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/nonlinear-heat-radiative-bcs-t-4-dim-40}},
note = {Self-reported vendor benchmark; internally generated by Resonix Labs and not independently verified. Accessed YYYY-MM-DD. Freeze 2026-08-13; libsolvsrk 2.3.0; SciPy 1.14.}
}TRL 4–5 · simulation-lab validated · 398 problems · 14 solver arms · clean + 5 noise levels
Freeze: 2026-08-13 · scipy 1.14 · libsolvsrk 2.3.0 · Methodology
Self-reported by Resonix Labs · not independently verified · Verification status