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Record W2049367060 · doi:10.1145/1356052.1356056

Algorithm 874

2008· article· en· W2049367060 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueACM Transactions on Mathematical Software · 2008
Typearticle
Languageen
FieldEngineering
TopicAdvanced Numerical Methods in Computational Mathematics
Canadian institutionsDalhousie UniversitySaint Mary's UniversityUniversity of Saskatchewan
Fundersnot available
KeywordsComputer scienceSolverDiscretizationAlgorithmMethod of linesSource lines of codeRunge–Kutta methodsSoftwareMathematical optimizationNumerical analysisApplied mathematicsMathematicsDifferential equationDifferential algebraic equationOrdinary differential equation

Abstract

fetched live from OpenAlex

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.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.962
Threshold uncertainty score0.954

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.001

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.

Opus teacher head0.038
GPT teacher head0.284
Teacher spread0.246 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it