Bibliographic record
Abstract
BACOL and BACOLR are (Fortran 77) B-spline adaptive collocation packages for the numerical solution of 1D parabolic Partial Differential Equations (PDEs). The packages have been shown to be superior to other similar packages, especially for problems exhibiting sharp, moving spatial layer regions, where a stringent tolerance is imposed. In addition to providing temporal error control through the timestepping software, BACOL and BACOLR feature control of a high-order estimate of the spatial error of the approximate solution, obtained by computing a second approximate solution of one higher order of accuracy; the cost is substantial—execution time and memory usage are almost doubled. In this article, we discuss BACOLI, a new version of BACOL that computes only one approximate solution and uses efficient interpolation-based schemes to obtain a spatial error estimate. In previous studies these schemes have been shown to provide spatial error estimates of comparable quality to those of BACOL. We describe the substantial modification of BACOL needed to obtain BACOLI, and provide numerical results showing that BACOLI is significantly more efficient than BACOL, in some cases by as much as a factor of 2. We also introduce a Fortran 95 wrapper for BACOLI (called BACOLI95) and discuss its simplified user interface.
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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) | 0.002 | 0.001 |
| 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 | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.159 | 0.072 |
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".