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Record W2580609865

High-order TVD and TVB linear multistep methods

2004· article· en· W2580609865 on OpenAlexfundno aff
Steven J. Ruuth, Willem Hundsdorfer

Bibliographic record

VenueData Archiving and Networked Services (DANS) · 2004
Typearticle
Languageen
FieldMathematics
TopicNumerical methods for differential equations
Canadian institutionsnot available
FundersCentrum Wiskunde and InformaticaNatural Sciences and Engineering Research Council of CanadaNederlandse Organisatie voor Wetenschappelijk OnderzoekEuropean Research Consortium for Informatics and Mathematics
KeywordsMonotonic functionTotal variation diminishingMathematicsBounded functionApplied mathematicsLinear multistep methodRunge–Kutta methodsMathematical optimizationNumerical analysisMathematical analysisDifferential equation
DOInot available

Abstract

fetched live from OpenAlex

We consider linear multistep methods that possess the TVD (total variation diminishing) or TVB (total variation bounded) properties, or related general monotonicity and boundedness properties. Strict monotonicity or TVD, in terms of arbitrary starting values for the multistep schemes, is only valid for a small class of methods, under very stringent step size restrictions. This makes them uncompetitive to the TVD Runge-Kutta methods. By relaxing these strict monotonicity requirements a larger class of methods can be considered, including many methods of practical interest. In this paper we construct linear multistep methods of high-order (up to six) that possess relaxed monotonicity or boundedness properties with optimal step size conditions. Numerical experiments show that the new schemes perform much better than the classical TVD multistep schemes. Moreover there is a substantial gain in efficiency compared to recently constructed TVD Runge-Kutta methods.

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.

How this classification was reachedexpand

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)0.001
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: Other design · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.927
Threshold uncertainty score0.957

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
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 science0.0010.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.073
GPT teacher head0.398
Teacher spread0.325 · 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

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designOther design
Domainnot available
GenreMethods

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".

Quick stats

Citations1
Published2004
Admission routes1
Has abstractyes

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