Numerical evaluation with the fractional Newton explicit group technique for a certain class of fractional partial differential equations
Bibliographic record
Abstract
The present paper gives an accurate technique for solving Caputo’s fractional Burger equations and fractional Fisher equations using the fractional Newton explicit group method. In this technique, the fractional derivative operator in the interval (0, 1) is approximated by an implicit finite difference scheme (FDM). Numerical simulations of the two models under study are presented by comparing the results for various values of the order of the fractional derivatives to estimate the accuracy and efficiency of the given technique for solving these two problems. The method is applied to the proposed equations to demonstrate the consistency of its achievement in solving such systems. Also, a comparison with the solutions of another technique for distinct quantities of the size of the matrices introduced in the same method, the calculation of the error, and the time taken are presented, through which we can confirm that the proposed method outperforms or complements the existing techniques. Finally, from the proposed numerical results, we can confirm the effectiveness of this technique in solving such real phenomena.
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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 | 0.000 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".