Certain New Models of the Multi-Space Fractal-Fractional Kuramoto-Sivashinsky and Korteweg-de Vries Equations
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Bibliographic record
Abstract
The main objective of this paper is to introduce and study the numerical solutions of the multi-space fractal-fractional Kuramoto-Sivashinsky equation (MSFFKS) and the multi-space fractal-fractional Korteweg-de Vries equation (MSFFKDV). These models are obtained by replacing the classical derivative by the fractal-fractional derivative based upon the generalized Mittag-Leffler kernel. In our investigation, we use the spectral collocation method (SCM) involving the shifted Legendre polynomials (SLPs) in order to reduce the new models to a system of algebraic equations. We then use one of the known numerical methods, the Newton-Raphson method (NRM), for solving the resulting system of the nonlinear algebraic equations. The efficiency and accuracy of the numerical results are validated by calculating the absolute error as well as the residual error. We also present several illustrative examples and graphical representations for the various results which we have derived in this paper.
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Full frame distilled prediction
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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)
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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