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The fractional non-polynomial spline method: Precision and modeling improvements

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  • Yousif, Majeed A.
  • Hamasalh, Faraidun K.

Abstract

This research introduces the fractional non-polynomial spline method as a novel scheme for solving the time-fractional Korteweg-de Vries (KdV) equation. The study focuses on numerical analysis and algorithm development for simulation purposes. The proposed method involves the construction of a fractional non-polynomial spline to estimate the equation's solution, offering improved precision and modeling capabilities compared to existing approaches. To assess the stability of the proposed approach, the von Neumann method is employed, demonstrating its unconditional stability within a specific parameter range. To validate the effectiveness of our numerical analysis and simulation algorithm, contour, 2D, and 3D graphs are utilized to compare the solution obtained through our method with an analytical solution. Through rigorous comparative analysis with previous works, the superiority of our approach in terms of accuracy and efficiency is demonstrated. Norm error calculations, specifically the (L2and L∞) error norms, provide a quantitative assessment of the accuracy and reliability of our proposed scheme.

Suggested Citation

  • Yousif, Majeed A. & Hamasalh, Faraidun K., 2024. "The fractional non-polynomial spline method: Precision and modeling improvements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 512-525.
    • Handle: RePEc:eee:matcom:v:218:y:2024:i:c:p:512-525
    DOI: 10.1016/j.matcom.2023.11.033
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    References listed on IDEAS

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    1. Shen, Jinye & Sun, Zhi-zhong & Cao, Wanrong, 2019. "A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 752-765.
    2. A. K. Gupta & S. Saha Ray, 2014. "On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-16, May.
    3. Berat Karaagac & Alaattin Esen & Kolade M. Owolabi & Edson Pindza, 2023. "A collocation method for solving time fractional nonlinear Korteweg–de Vries–Burgers equation arising in shallow water waves," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(07), pages 1-16, July.
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    Cited by:

    1. Ying-Ying Yu & Xin Li & Ye Ji, 2024. "On Intersections of B-Spline Curves," Mathematics, MDPI, vol. 12(9), pages 1-17, April.
    2. Abdelouahed Kouibia & Miguel Pasadas & Loubna Omri, 2024. "A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces," Mathematics, MDPI, vol. 12(11), pages 1-11, June.
    3. Cemil Tunç & Fahir Talay Akyildiz, 2024. "Unique Solutions for Caputo Fractional Differential Equations with Several Delays Using Progressive Contractions," Mathematics, MDPI, vol. 12(18), pages 1-15, September.
    4. Xin Song & Rui Wu, 2024. "An Efficient Numerical Method for Solving a Class of Nonlinear Fractional Differential Equations and Error Estimates," Mathematics, MDPI, vol. 12(12), pages 1-12, June.

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