Overview Evidence tour Methodology Dead zones Problems

Arenstorf orbit

DISADVANTAGES0 · dim 4

A baseline wins. At the comparison noise level, the best baseline beats SolvSRK by at least 10 percentage points of survival, or by at least 0.05 balanced score when survival is tied. Use the winning baseline named on the problem page - not SolvSRK. All verdicts →

A restricted three-body periodic orbit requiring tight tolerances over a long integration. Published as a disadvantage case: SolvSRK wins clean but loses under noise.

Oscillators & nonlinear dynamics

Problem definition

Arenstorf (1963); Hairer–Wanner I §I.16

Math used in the published benchmark cell - so you can confirm the name matches the ODE you expect. Not a runnable fixture.

ẋ = u
ẏ = v
u̇ = x + 2 v − μ′ (x + μ) / D₁ − μ (x − μ′) / D₂
v̇ = y − 2 u − μ′ y / D₁ − μ y / D₂
D₁ = ((x + μ)² + y²)^(3/2)
D₂ = ((x − μ′)² + y²)^(3/2)
μ′ = 1 − μ

Parameters: μ = 0.012277471
Initial condition: (x, u, y, v)(0) = (0.994, 0, 0, −2.00158510637908252)
Horizon: t ∈ [0, 17.0652165601579625] (one periodic orbit)

Restricted three-body Arenstorf orbit written in first-order form (state = position + velocity). Non-stiff; long tight-tolerance integration.

Fingerprint

Spread: low

Default noise: clean

Recommendation snapshot

Clean best: SolvSRK

Noisy best: SciPy

Coverage

14 solver arms · clean + 5 noise levels

Ranked on survival, precision, and speed

Versions & freeze

Methodology →

Freeze: 2026-08-13
libsolvsrk: 2.3.0
SciPy: 1.14
SUNDIALS: CVODE (bundled backend)

20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: Arenstorf orbit (arenstorf)

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

Results matrix

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%	6.4	5,730	33 ms	0.770
2	SciPy RadauSciPy	100%	6.0	10,521	203 ms	0.763
3	Vern7external	100%	5.4	2,372	3.83 s	0.749
4	Vern9external	100%	4.7	2,114	3.80 s	0.730
5	Tsit5external	100%	4.4	2,418	922 ms	0.724
6	SciPy DOP853SciPy	100%	4.4	1,778	13 ms	0.723
7	FBDFexternal	100%	4.2	2,033	4.84 s	0.720
8	SciPy RK45SciPy	100%	4.1	2,114	16 ms	0.717
9	SciPy RK23SciPy	100%	3.6	11,465	108 ms	0.705
10	CVODE Adamsexternal	100%	3.3	1,004	14 ms	0.697
11	SciPy LSODASciPy	100%	3.0	1,365	7 ms	0.691
12	SciPy BDFSciPy	100%	2.6	2,813	92 ms	0.682
13	CVODE BDFexternal	100%	2.3	1,346	17 ms	0.675
14	TRBDF2external	100%	0.2	9,378	5.00 s	0.623

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 →

Cite this page

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_arenstorf_2026,
  title        = {Resonix Evidence Portal: Arenstorf orbit},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/arenstorf}},
  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