The meshless method for two-dimensional space-time fractional dispersion equation based on reproducing kernel particle method
Bibliographic record
Abstract
The two-dimensional space fractional dispersion equation (SFDE) is obtained from the standard dispersion equation by replacing the two second-order space derivatives by the Riemann–Liouville fractional derivatives. A numerical analysis of the two-dimensional SFDE is presented based on the reproducing kernel particle method (RKPM). The final algebraic equation system is obtained by employing Galerkin weak form and functional minimization procedure. The Riemann–Liouville operator is discretized by the shifted Grünwald formula. The fully-discrete approximation schemes for SFDE are established using center difference method and RKPM and the shifted Grünwald formula. Numerical simulations for SFDE with known exact solution were presented in the format of the tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error estimate of RKPM for SFDE has been analyzed, which shows that this method has reasonable convergence rates in spatial and temporal discretizations.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".