Fractional Clique Collocation Technique for Numerical Simulations of Fractional-Order Brusselator Chemical Model
Bibliographic record
Abstract
The primary focus of this research study is in the development of an effective hybrid matrix method to solve a class of nonlinear systems of equations of fractional order arising in the modeling of autocatalytic chemical reaction problems. The fractional operator is considered in the sense of Liouville–Caputo. The proposed approach relies on the combination of the quasi-linearization technique and the spectral collocation strategy based on generalized clique bases. The main feature of the hybrid approach is that it converts the governing nonlinear fractional-order systems into a linear algebraic system of equations, which is solved in each iteration. In a weighted L2 norm, we prove the error and convergence analysis of the proposed algorithm. By using various model parameters in the numerical examples, we show the computational efficacy as well as the accuracy of our approach. Comparisons with existing available schemes show the high accuracy and robustness of the designed hybrid matrix collocation technique.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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 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".