A Chebyshev Based Spectral Method for Solving Boundary Layer Flow of a Fractional-Order Oldroyd-B Fluid
Bibliographic record
Abstract
We focused on developing an accurate numerical scheme for the flow of a fractionalorder Oldroyd-B fluid model with the non-isothermal property. In many cases, the direct application of the Chebyshev tau method using the operational matrix of the Chebyshev polynomials usually leads to an accurate solution. However, in some cases, dealing with non-linearity and coupling can be tedious. In this study, we present a numerical method based on Chebyshev polynomials of the first kind and interpolation using Gauss-Lobatto quadrature. The coefficients of the series expansion of the pseudospectral method are obtained through integration of the Chebyshev polynomials orthogonality condition. The numerical results show that the scheme is accurate and reliable. The effects of the fractional-order objective stress rate of the Oldroyd-B fluid on the velocity and shear stress are also presented. The error bound theorems presented in this study support the findings of the numerical computations.
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 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) | 0.000 | 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".