Numerical Finite Difference Scheme for a Two-Dimensional Time-Fractional Semilinear Diffusion Equation
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Bibliographic record
Abstract
Time-fractional partial differential equations are foundational instruments in modeling neuronal dynamics.These equations are formulated by replacing the conventional time derivative of order α, where 0 < < 1, in the standard equation with the Caputo fractional derivative.This study introduces the Crank-Nicolson (C.N.) finite difference scheme as a solution method for a two-dimensional, time-fractional Semilinear parabolic equation under Dirichlet boundary conditions.An in-depth investigation into the consistency, stability, and convergence of the proposed scheme is also conducted.To corroborate the theoretical findings, two numerical experiments are carried out.The scheme's efficiency, in terms of absolute errors, order of accuracy, and computational time, is meticulously evaluated and discussed.The results demonstrate that the proposed scheme, while being conditionally stable, can be utilized effectively with a high rate of convergence to compute numerical solutions for the problem at hand.
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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 | 0.001 | 0.001 |
| 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 it