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NUMERICAL SOLUTIONS OF SPACE FRACTIONAL VARIABLE-COEFFICIENT KdV–MODIFIED KdV EQUATION BY FOURIER SPECTRAL METHOD

Author

Listed:
  • CHE HAN

    (Department of Mathematics, Inner Mongolia University of Technology, Hohhot, 010051, P. R. China)

  • YU-LAN WANG

    (Department of Mathematics, Inner Mongolia University of Technology, Hohhot, 010051, P. R. China)

  • ZHI-YUAN LI

    (Department of Mathematics, Inner Mongolia University of Technology, Hohhot, 010051, P. R. China)

Abstract

Today, most of the real physical world problems can be modeled with variable-coefficient KdV–modified KdV (vcKdV–mKdV) equation. Besides, the solution methods and their reliabilities are the most important. Therefore, a high precision numerical method is always needed. In this paper, Fourier spectral method is applied to solve the space fractional generalized vcKdV–mKdV equation and the influence of fractional orders on numerical solution of the space fractional generalized vcKdV–mKdV equation is investigated. Numerical simulations in different situations of equation are conducted, including the propagation and interaction of the generalized ball-type, kink-type and periodic-depression solitons. From the numerical experiments pondered here and compared with the other methods, it is found that the numerical solutions match well with the exact solutions, which demonstrate that the Fourier spectral method is a satisfactory and efficient algorithm.

Suggested Citation

  • Che Han & Yu-Lan Wang & Zhi-Yuan Li, 2021. "NUMERICAL SOLUTIONS OF SPACE FRACTIONAL VARIABLE-COEFFICIENT KdV–MODIFIED KdV EQUATION BY FOURIER SPECTRAL METHOD," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-19, December.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:08:n:s0218348x21502467
    DOI: 10.1142/S0218348X21502467
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    Cited by:

    1. Che, Han & Wang, Yu-Lan & Li, Zhi-Yuan, 2022. "Novel patterns in a class of fractional reaction–diffusion models with the Riesz fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 149-163.
    2. He, Ji-Huan & Jiao, Man-Li & Gepreel, Khaled A. & Khan, Yasir, 2023. "Homotopy perturbation method for strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 243-258.
    3. Ain, Qura tul & Khan, Aziz & Ullah, Muhammad Irfan & Alqudah, Manar A. & Abdeljawad, Thabet, 2022. "On fractional impulsive system for methanol detoxification in human body," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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