Efficient simulation of Time-Fractional Korteweg-de Vries equation via conformable-Caputo non-Polynomial spline method

Majeed A Yousif, Faraidun K Hamasalh, Ahmad Zeeshan and Mohamed Abdelwahed

PLOS ONE, 2024, vol. 19, issue 6, 1-18

Abstract: This research presents a novel conformable-Caputo fractional non-polynomial spline method for solving the time-fractional Korteweg-de Vries (KdV) equation. Emphasizing numerical analysis and algorithm development, the method offers enhanced precision and modeling capabilities. Evaluation via the Von Neumann method demonstrates unconditional stability within defined parameters. Comparative analysis, supported by contour and 2D/3D graphs, validates the method’s accuracy and efficiency against existing approaches. Quantitative assessment using L2 and L∞ error norms confirms its superiority. In conclusion, the study proposes a robust solution for the time-fractional KdV equation.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0303760

DOI: 10.1371/journal.pone.0303760

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