Efficient Solutions for Nonlinear Diffusion Equations Appeared as Models of Physical Problems
Bibliographic record
Abstract
The differential transform technique (DTM) looks promise for dealing with functional problems. Recent articles have demonstrated the DTM's efficiency in tackling a wide range of issues in many disciplines. In this paper, (DTM) is used to develop approximate, and exact solutions for some nonlinear diffusion equations. Nonlinear diffusion equations are used to describe processes and behaviours in fields of biology, heat transfer, chemical reactions, and mathematical physics. The differential transform method linked with Laplace transform and Pad’e approximation is used to improve some known results. The obtained solutions are compared with the exact known solutions, showing excellent agreement. The differential transformation method was used in conjunction with the use of the Laplace transform and the Pad’e approximation method, for the purpose of improving some calculations in the hope of obtaining a more accurate solution. The results were presented in the form of tables or graphics for the purpose of comparing the calculated solution and comparing it with some of the precise solutions presented previously. The results showed the accuracy of the agreement between the two solutions. This gives us the opportunity to use the method under consideration to find solutions to unknown problems and thus ensure the credibility of the calculated solution.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".