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Brusselator 1-D PDE (N=100)

PARITYS2 · dim 200

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 →

Method-of-lines discretisation of 1-D Brusselator PDE, 100 cells (dim=200)

Chemistry & reaction kinetics

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 _brusselator_1d_rhs(t, y, N=100, A=1.0, B=3.0, alpha=0.02):
    """1D Brusselator reaction-diffusion, method of lines."""
    dim = 2 * N
    u = y[:N]
    v = y[N:]
    dx = 1.0 / (N + 1)
    dx2 = dx * dx
    du = np.zeros(N)
    dv = np.zeros(N)
    for i in range(N):
        u_left = u[i-1] if i > 0 else 1.0
        u_right = u[i+1] if i < N-1 else 1.0
        v_left = v[i-1] if i > 0 else 3.0
        v_right = v[i+1] if i < N-1 else 3.0
        du[i] = alpha / dx2 * (u_left - 2*u[i] + u_right) + A + u[i]**2 * v[i] - (B+1)*u[i]
        dv[i] = alpha / dx2 * (v_left - 2*v[i] + v_right) + B*u[i] - u[i]**2 * v[i]
    return np.concatenate([du, dv])

def rhs(t, y):
    return _brusselator_1d_rhs(t, y, N=100)
Parameters
  • A = 1
  • B = 3
  • alpha = 0.02
  • N = 100
Initial condition
y(0) = [1, 1, 1, 1, 1, 1, …] [shape=(200,), min=1, max=3]
Horizon
t ∈ [0, 10]

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: high

Default noise: low

Recommendation snapshot

Clean best: SciPy BDF

Noisy best: SciPy BDF

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: Brusselator 1-D PDE (N=100) (brusselator-1-d-pde-n-100)

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

#SolverSurvivalSCDnfevWallScore
1SciPy BDFSciPy
100%
16.021847 ms1.000
2SciPy RadauSciPy
100%
16.023456 ms1.000
3SciPy RK45SciPy
100%
16.05010 ms1.000
4SciPy LSODASciPy
100%
16.04<1 ms1.000
5SciPy DOP853SciPy
100%
16.09820 ms1.000
6SciPy RK23SciPy
100%
16.0265 ms1.000
7CVODE BDFexternal
100%
16.020654 ms1.000
8CVODE Adamsexternal
100%
16.020656 ms1.000
9Tsit5external
100%
16.024849 ms1.000
10SolvSRK
100%
16.021454 ms1.000

At Clean, best balanced arm is SciPy BDF · SolvSRK survival 100%, SCD 16.0.

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_brusselator_1_d_pde_n_100_2026,
  title        = {Resonix Evidence Portal: Brusselator 1-D PDE (N=100)},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/brusselator-1-d-pde-n-100}},
  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.}
}

Related

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