On the Numerical Solution of the Basic Equation of Wave Mechanics with the Gerasimov – Caputo Fractional Derivative
Bibliographic record
Abstract
Subject of research: initial-boundary value problem for the fundamental equation of fractional wave mechanics with fractional Gerasimov – Kaputo time derivative and the influence of the numerical solution parameters on the accuracy and stability of quantum system modeling. Purpose of research: to conduct numerical experiments to illustrate the accuracy and efficiency of the proposed scheme, demonstrating its applicability to problems involving fractional quantum dynamics. Research methods: the matrix sweep method and multidimensional modeling are used to approximate the solution, a corresponding finite-difference scheme is constructed; special attention is paid to the algorithm of the constructed numerical scheme and the assessment of the influence of fractional parameters on the accuracy and stability of the solution. Objects of research: numerical solution of the fundamental equation of wave mechanics with fractional Gerasimov – Kaputo time derivative as a mathematical model of quantum processes. Research findings: the obtained numerical data allow us to identify patterns of changes in the system's behavior depending on the characteristics of fractional differentiation, which is especially important in modeling complex physical processes. The results provide insight into the behavior of the solution and contribute to the development of reliable computational methods for fractional differential equations. The developed technique can be applied to a wide class of problems, including modeling of transport processes, wave phenomena, and quantum dynamics in systems with anomalous diffusion. The proposed approaches open up new possibilities for studying fractional time systems and can be useful in developing high-precision numerical algorithms.
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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 | 0.001 | 0.002 |
| 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".