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

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  • Majeed A Yousif
  • Faraidun K Hamasalh
  • Ahmad Zeeshan
  • Mohamed Abdelwahed

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.

Suggested Citation

  • Majeed A Yousif & Faraidun K Hamasalh & Ahmad Zeeshan & Mohamed Abdelwahed, 2024. "Efficient simulation of Time-Fractional Korteweg-de Vries equation via conformable-Caputo non-Polynomial spline method," PLOS ONE, Public Library of Science, vol. 19(6), pages 1-18, June.
    • Handle: RePEc:plo:pone00:0303760
    DOI: 10.1371/journal.pone.0303760
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    References listed on IDEAS

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    1. Marin Marin & Aatef Hobiny & Ibrahim Abbas, 2021. "The Effects of Fractional Time Derivatives in Porothermoelastic Materials Using Finite Element Method," Mathematics, MDPI, vol. 9(14), pages 1-14, July.
    2. Turkyilmazoglu, Mustafa & Altanji, Mohamed, 2023. "Fractional models of falling object with linear and quadratic frictional forces considering Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
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