One-step strong-stability-preserving Hermite-Birkhoff-Taylor methods
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Bibliographic record
Abstract
We construct new one-step explicit multistage strong-stability-preserving (SSP) Hermite–Birkhoff–Taylor (HBT) time discretization methods of orders 3 to 5 for integrating hyperbolic conservation laws. The methods use derivatives y′ and y′′ as in Taylor methods of order two combined with Runge–Kutta (RK) methods of orders 2 to 4. Compared to RK methods of the same order and with the same number of stages, the new methods generally have larger SSP coefficients on Burgers’ equations. Moreover, these SSP HBT methods have stage order two, compared to stage order one for RK methods and hence are less susceptible to order reduction from source terms or nonhomogeneous boundary conditions.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it