2008.05734
A Newton interpolation based predictor-corrector numerical method for fractional differential equations with an activator-inhibitor case study
Redouane Douaifia, Samir Bendoukha, Salem Abdelmalek
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The candidate solution reconstructs the paper’s derivation: it starts from the Caputo integral form, partitions [0,t_{m+1}] into subintervals, approximates f by Newton polynomials (with the same delayed/anchored choices as in the paper), and evaluates the same kernel-weighted polynomial integrals to obtain the improved explicit predictor and the implicit corrector whose ym+1 terms are then replaced by the predictor. The resulting weights and sums match the paper’s predictor (its Eq. (44)) and corrector (its Eq. (45)) exactly, and the auxiliary quantity Υ_{m−1} matches Eq. (33) in the paper. No logical gaps beyond those already present in the paper (e.g., lack of a full error/stability analysis) were found. See the paper’s formulas and derivation around Eqs. (33), (41)–(45) for the exact expressions the model reproduces .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
A well-executed, implementable derivation of an improved predictor-corrector scheme based on Newton interpolation for fractional IVPs is presented. The main contribution is an explicit, higher-fidelity predictor obtained by retaining additional terms, with a compatible corrector. The model’s reconstruction confirms algebraic correctness. To strengthen the work, a brief analytical discussion of accuracy and stability, clearer start-up treatment, and a concise summary of weights would be valuable.