@article{Huntul2025, 
author = {M. J. Huntul},
title = {Bell polynomial-based semi-discretization approach for the extended Fisher-Kolmogorov equations},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {29263-29284},
keywords = {Bell polynomials, Taylor approach, extended Fisher-Kolmogorov equation, collocation nodes, error analysis},
url = {https://www.sciopen.com/article/10.3934/math.20251286},
doi = {10.3934/math.20251286},
abstract = {This work introduces an integrated numerical framework for obtaining numerical approximations to the extended Fisher-Kolmogorov (EFK) equation model. The methodology entails a two-stage process: initial linearization of the governing equation through a Taylor series approach, followed by the application of a spectral collocation method utilizing Bell polynomials to resolve the resultant linear system. Comprehensive theoretical considerations, including a detailed error estimate in the weighted        L    2  -norm, are established. The numerical investigation, comprising three illustrative test cases, confirms the scheme's computational efficiency and demonstrates a marked improvement in accuracy when compared to current state-of-the-art results and exact solutions.}
}