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Performance of a hybrid computational scheme on traveling waves and its dynamic transition for Gilson–Pickering equation

Author

Listed:
  • Turgut Ak

    (Armutlu Vocational School, Yalova University, Armutlu, 77500 Yalova, Turkey)

  • Asit Saha

    (Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, East-Sikkim 737136, India)

  • Sharanjeet Dhawan

    (Department of Mathematics, Central University of Haryana, 123029 Haryana, India)

Abstract

In this work, we developed a hybrid scheme for Gilson–Pickering equation by extracting advantageous features of collocation method and B-splines. Collocation method involves satisfying a differential equation to some tolerance at finite number of points and has low computational cost. The idea is to extract the superior accuracy and smoothness of B-spline functions with the low computational cost of collocation scheme. In the vision of a superficial periodic force, we obtain the quasiperiodic and chaotic behaviors of the forced Gilson–Pickering equation by perusing phase portrait technique, time series and Poincaré section. The sequel of frequency (ω) of the superficial periodic force is very prime in case of transition from weakly chaotic feature to quasiperiodic feature of the forced Gilson–Pickering equation.

Suggested Citation

  • Turgut Ak & Asit Saha & Sharanjeet Dhawan, 2019. "Performance of a hybrid computational scheme on traveling waves and its dynamic transition for Gilson–Pickering equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-17, April.
    • Handle: RePEc:wsi:ijmpcx:v:30:y:2019:i:04:n:s0129183119500281
    DOI: 10.1142/S0129183119500281
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    Cited by:

    1. Wensheng Chen & Jalil Manafian & Khaled Hussein Mahmoud & Abdullah Saad Alsubaie & Abdullah Aldurayhim & Alabed Alkader, 2023. "Cutting-Edge Analytical and Numerical Approaches to the Gilson–Pickering Equation with Plenty of Soliton Solutions," Mathematics, MDPI, vol. 11(16), pages 1-35, August.

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