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Meshless spectral method for solution of time-fractional coupled KdV equations

Author

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  • Hussain, Manzoor
  • Haq, Sirajul
  • Ghafoor, Abdul

Abstract

In this article, an efficient and accurate meshless spectral interpolation method is formulated for the numerical solution of time-fractional coupled KdV equations that govern shallow water waves. Meshless shape functions constructed via radial basis functions (RBFs) and point interpolation are used for discretization of the spatial operator. Approximation of fractional temporal derivative is obtained via finite differences of order O(τ2−α) and a quadrature formula. The formulated method is applied to various test problems available in the literature for its validation. Approximation quality and efficiency of the method is measured via discrete error norms E2, E∞ and Erms. Convergence analysis of the proposed method in space and time is numerically determined by varying nodal points M and time step-size τ respectively. Stability of the proposed method is discussed and affirmed computationally, which is an important ingredient of the current study.

Suggested Citation

  • Hussain, Manzoor & Haq, Sirajul & Ghafoor, Abdul, 2019. "Meshless spectral method for solution of time-fractional coupled KdV equations," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 321-334.
    • Handle: RePEc:eee:apmaco:v:341:y:2019:i:c:p:321-334
    DOI: 10.1016/j.amc.2018.09.001
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    References listed on IDEAS

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    1. Abdon Atangana & Aydin Secer, 2013. "The Time-Fractional Coupled-Korteweg-de-Vries Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, March.
    2. Haq, Sirajul & Hussain, Manzoor, 2018. "Selection of shape parameter in radial basis functions for solution of time-fractional Black–Scholes models," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 248-263.
    3. Shivanian, Elyas & Jafarabadi, Ahmad, 2018. "An improved meshless algorithm for a kind of fractional cable problem with error estimate," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 138-151.
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    Cited by:

    1. Arifeen, Shams Ul & Haq, Sirajul, 2023. "Petrov–Galerkin approximation of time-fractional coupled Korteweg–de Vries equation for propagation of long wave in shallow water," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 226-242.

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