A robust numerical approximation of advection diffusion equations with nonsingular kernel derivative
Bibliographic record
Abstract
Abstract In this article we aim to approximate linear time fractional advection diffusion equations (TFADE) with Atangana-Baleanu- Caputo(ABC) derivative using local meshless method and Laplace transformation(LT). The method comprises of three steps. In the first step the the time variable is eliminated using LT. In the second step the reduced problem is solved using local meshless method. In the third step the solution of TFADE with ABC derivative is retrieved from local meshless methods solution by representing it as Bromwich integral. We then approximate the integral using some suitable quadrature rule. The stability and convergence of the method are discussed. The local meshless method is utilized to overcome the ill-conditioning issue of the interpolation matrices in global meshless methods and to over come the shape parameters sensitivity. Also in comparison with time stepping methods the LT is employed and contour integration technique is utilized to deal with the ABC derivative, which circumvent the calculation of costly convolution integrals in the approximation of ABC derivative, and also avoids the effect of time step on the stability and accuracy. Some test problems are considered in one and two dimensions to validate the proposed numerical method. The two dimensional problem is solved in regular and irregular domains. The computational experiments confirms that this method is computationally efficient and highly accurate for such type of problems.
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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 | 0.000 | 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".