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A new approach for the numerical approximation of modified Korteweg–de Vries equation

Author

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  • Ahmad, Fayyaz
  • Ur Rehman, Shafiq
  • Zara, Aiman

Abstract

We present and illustrate a new numerical scheme for the numerical approximation of modified Korteweg–de Vries (mKdV) equation. The spatial derivatives involved in the modified Korteweg–de Vries equation are approximated by smoothing Kernel technique. Whereas, for the time integration, we use Crank–Nicolson integrator. The constant of mass conservation (I1), constant of energy conservation (I2), and the constant of momentum conservation (I3) provide much insight about the conservative nature of the proposed numerical scheme. The numerical testing is performed on a collection of three test problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:189-206
    DOI: 10.1016/j.matcom.2022.06.021
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    References listed on IDEAS

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    1. 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.
    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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    1. 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.
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