Bibliographic record
Abstract
In this article we discuss a new software package, BACOLR, for the numerical solution of a general class of time-dependent 1-D PDEs. This package employs high-order adaptive methods in time and space within a method-of-lines approach and provides tolerance control of the spatial and temporal errors. The DAEs resulting from the spatial discretization (based on B-spline collocation) are handled by a substantially modified version of the Runge-Kutta solver, RADAU5. For each time step, the RADAU5 code computes an estimate of the temporal error and requires it to satisfy the user tolerance. After each time step BACOLR then computes a high-order estimate of the spatial error and requires this error estimate to satisfy the user tolerance. BACOLR was developed through a substantial modification of the adaptive method-of-lines package, BACOL. In this article we introduce the BACOLR package and present numerical results to show that the performance of BACOLR is comparable to and in some cases significantly superior to that of BACOL, which was shown in previous work to be more efficient, reliable and robust than other existing codes, especially for problems with solutions exhibiting narrow spikes or boundary layers.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.100 | 0.043 |
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 source (direct Gemma or distilled Codex), 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".