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Numerical approximation of modified Kawahara equation using Kernel smoothing method

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  • Zara, Aiman
  • Rehman, Shafiq Ur
  • Ahmad, Fayyaz
  • Kouser, Salima
  • Pervaiz, Anjum

Abstract

In this article, a numerical approximation of modified Kawahara equation is investigated by Kernel smoothing method. The spatial derivatives involved in the modified Kawahara equation are approximated by smoothing Kernel method. Whereas, for the time integration, we employ Crank–Nicolson method. The conservative nature of the proposed scheme is demonstrated by the mass conservation constant (I1) and energy conservation constant (I2). To quantify the quality of the proposed scheme, we also have performed numerical testing on a collection of test problems.

Suggested Citation

  • Zara, Aiman & Rehman, Shafiq Ur & Ahmad, Fayyaz & Kouser, Salima & Pervaiz, Anjum, 2022. "Numerical approximation of modified Kawahara equation using Kernel smoothing method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 169-184.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:169-184
    DOI: 10.1016/j.matcom.2021.11.014
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    References listed on IDEAS

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    1. Nur Hasan Mahmud Shahen & Foyjonnesa & Md Habibul Bashar & Tasnim Tahseen & Sakhawat Hossain, 2021. "Solitary and Rogue Wave Solutions to the Conformable Time Fractional Modified Kawahara Equation in Mathematical Physics," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-9, July.
    2. Zehra Pınar & Turgut Öziş, 2013. "The Periodic Solutions to Kawahara Equation by Means of the Auxiliary Equation with a Sixth-Degree Nonlinear Term," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, March.
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    Cited by:

    1. Ahmad, Fayyaz & Ur Rehman, Shafiq & Zara, Aiman, 2023. "A new approach for the numerical approximation of modified Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 189-206.

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