SOLVING TIME-FRACTIONAL FISHER MODELS BY NON-POLYNOMIAL SPLINES IN TERMS OF LOGARITHMIC DERIVATIVES
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Bibliographic record
Abstract
This paper introduces a novel numerical approach, the logarithmic non-polynomial spline method (LNPSM), leveraging a non-polynomial spline function with logarithmic terms to solve the conformable time-fractional Fisher (TFF) equation. The developed scheme achieves six-order convergence, derived through truncation error analysis and the Taylor series expansion. Stability is ensured under conditional constraints verified by von Neumann stability analysis. The method’s accuracy is demonstrated through two test examples, with results presented in comparison tables alongside cubic B-spline and Caputo non-polynomial spline methods, evaluated by norm errors. Additionally, graphical representations, including 2D and 3D plots, further illustrate the effectiveness of LNPSM. The findings indicate that LNPSM is a suitable and robust tool for solving time-fractional differential equations.
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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 | 0.000 |
| 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) | 0.001 | 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 it