Strong-Stability-Preserving Hermite—Birkhoff Time-Discretizations of Order 4 to 12
Bibliographic record
Abstract
Optimal strong‐stability‐preserving Hermite—Birkhoff (SSP HB) methods, HBksp, of order p = 4,5,...,12 have been constructed by combining k‐step methods of order p = 1,2,...,9 and s‐stage Runge—Kutta (RK) methods of order 4, with s = 4,5,...,10. These methods are well suited for solving discretized hyperbolic PDEs by the methods of lines. The Shu—Osher representation of RK methods is extended to the above SSP HB methods. The HBksp having the largest effective SSP coefficient have been found numerically among the HB methods of order p on hand. Several high‐order SSP HB methods are compared with SSP RK methods of order 4.
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How this classification was reachedexpand
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 | 0.000 | 0.005 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".