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 →
The maximum-stiffness Van der Pol oscillator used as an integrator stress test. Included as a parity case — both SolvSRK and the best SciPy arm survive noise here.
Van der Pol (1920); Hairer–Wanner II §IV.2
Math used in the published benchmark cell — so you can confirm the name matches the ODE you expect. Not a runnable fixture.
ẋ = v v̇ = μ (1 − x²) v − x
Extreme-stiffness Van der Pol. Distinct from milder catalog entries (μ = 1, 100, 1000).
Fingerprint
Spread: extreme
Default noise: clean
Recommendation snapshot
Clean best: SciPy Radau (precision)
Noisy best: parity (SolvSRK ≈ SciPy)
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: Van der Pol (μ=10⁴) (vdpol_1e4)
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 | SciPy RadauSciPy | 100% | 15.3 | 150 | 3 ms | 0.985 |
| 2 | SolvSRK | 100% | 12.7 | 583 | 318 ms | 0.922 |
| 3 | SciPy LSODASciPy | 100% | 10.7 | 99 | <1 ms | 0.874 |
| 4 | SciPy RK23SciPy | 100% | 9.4 | 71,693 | 559 ms | 0.844 |
| 5 | SciPy RK45SciPy | 100% | 9.3 | 126,878 | 755 ms | 0.840 |
| 6 | Tsit5external | 100% | 9.0 | 130,620 | 10.51 s | 0.834 |
| 7 | SciPy BDFSciPy | 100% | 9.0 | 137 | 5 ms | 0.833 |
| 8 | CVODE BDFexternal | 100% | 8.9 | 73 | 6 ms | 0.831 |
| 9 | CVODE Adamsexternal | 100% | 8.8 | 235 | 7 ms | 0.828 |
| 10 | SciPy DOP853SciPy | 100% | 8.5 | 112,754 | 610 ms | 0.821 |
At Clean, best balanced arm is SciPy Radau · SolvSRK survival 100%, SCD 12.7.
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_vdpol_1e4_2026,
title = {Resonix Evidence Portal: Van der Pol (μ=10⁴)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/vdpol_1e4}},
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