Overview Evidence tour Methodology Dead zones Problems

Piecewise-linear 3-regime system

BOUNDARYS1 · dim 4

Partial / unstable. SolvSRK survives more than 0% but less than 90% of runs at the comparison noise level, without being beaten by a baseline there. Usable with margin and monitoring; validate on your own configuration. All verdicts →

Three-zone piecewise linear ODE; tests switching dynamics with mild stiffness

Oscillators & nonlinear dynamics

Problem definition

Canonical benchmark implementation

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.

Show canonical RHS excerpt

def _piecewise_linear_rhs(t, y):
    """3-regime piecewise linear: stiffness changes at x1 boundaries."""
    x1, x2, x3, x4 = y
    if x1 > 1.0:
        A = np.array([[-1, 0.5, 0, 0], [0, -10, 0.5, 0],
                       [0, 0, -100, 0.5], [0, 0, 0, -1000]])
    elif x1 < -1.0:
        A = np.array([[-1000, 0.5, 0, 0], [0, -100, 0.5, 0],
                       [0, 0, -10, 0.5], [0, 0, 0, -1]])
    else:
        A = np.array([[-1, 1, 0, 0], [0, -1, 1, 0],
                       [0, 0, -1, 1], [0, 0, 0, -1]])
    return A @ y

Parameters: No captured parameters; constants are explicit in the RHS excerpt.
Initial condition: y(0) = [2, 1, 0.5, 0.1]
Horizon: t ∈ [0, 20]

Canonical 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: low

Default noise: none

Recommendation snapshot

Clean best: SciPy DOP853

Noisy best: SolvSRK

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: Piecewise-linear 3-regime system (piecewise-linear-3-regime-system)

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	SciPy DOP853SciPy	100%	4.3	1,922	14 ms	0.721
2	Vern9external	100%	3.5	3,554	3.65 s	0.704
3	SolvSRK	100%	3.4	1,908	31 ms	0.701
4	Vern7external	100%	2.9	2,332	3.59 s	0.689
5	SciPy RadauSciPy	100%	1.7	2,397	48 ms	0.659
6	SciPy LSODASciPy	100%	1.6	778	4 ms	0.658
7	SciPy BDFSciPy	100%	0.7	817	28 ms	0.634
8	SciPy RK45SciPy	100%	0.6	1,982	16 ms	0.633
9	CVODE Adamsexternal	100%	0.6	682	12 ms	0.632
10	FBDFexternal	100%	0.4	729	4.63 s	0.629
11	Tsit5external	100%	0.4	2,076	818 ms	0.629
12	TRBDF2external	100%	0.1	1,406	4.69 s	0.622
13	CVODE BDFexternal	100%	0.1	538	10 ms	0.621
14	SciPy RK23SciPy	100%	0.0	2,681	26 ms	0.619

At Clean, best balanced arm is SciPy DOP853 · SolvSRK survival 100%, SCD 3.4.

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 →

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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_piecewise_linear_3_regime_system_2026,
  title        = {Resonix Evidence Portal: Piecewise-linear 3-regime system},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonix.tech/evidence/problems/piecewise-linear-3-regime-system}},
  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