Design and Analysis of NSFD Methods for the Diffusion-Free Brusselator
Bibliographic record
Abstract
This chapter reports on the design and analysis of two non-standard finite-difference (NSFD) methods for solving the diffusion-free Brusselator system. The first NSFD method is simulated using two different denominator functions. It is shown that, under certain conditions, the first method exhibits spurious behaviour, such as failing to capture the correct asymptotic stability properties of the unique fixed-point as well as the stable limit cycle of the continuous-time diffusion-free Brusselator system. On the other hand, the second NSFD method, designed using a semi-exact discretization framework of Mickens, is shown to be elementary stable and dynamically consistent with the diffusion-free Brusselator system for sufficiently small timesteps. These theoretical results are illustrated via numerical simulations.
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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 | 0.004 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".