HIGHER-ORDER METHOD FOR SOLVING FREE BOUNDARY-VALUE PROBLEMS
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Bibliographic record
Abstract
Abstract We present an extended one-step method of order 5 for the solution of the third-order, nonlinear free boundary-value problem. The Falkner-Skan equation as well as the Blasius equation are special cases of this problem. We prove that this method is A- and L-stable. The method uses a coordinate transformation to map a semi-infinite physical domain to the open unit interval (0, 1). Comparisons are made between the numerical solutions obtained by the proposed method and those obtained by previous authors. The author is indebted to Prof. S. E. El-Gendi and Prof. I. A. Hassanien for various valuable suggestions and constructive criticism. We express our gratitude to the (unknown) referees for their comments and suggestions.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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