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A collocation algorithm based on septic B-splines and bifurcation of traveling waves for Sawada–Kotera equation

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  • Karakoc, Seydi Battal Gazi
  • Saha, Asit
  • Sucu, Derya Yıldırım

Abstract

In present work, a mathematical model standing for the numerical solutions of the nonlinear Sawada–Kotera (S–K) equation has been examined. For this purpose, we have used collocation finite element method for the model problem. The solution for each unknown is written as a linear combination of time parameters and combination of the septic B-splines. Next, applying Von-Neumann theory, we demonstrate that the scheme is marginally stable. Error norms L2 and L∞ are computed for single soliton solutions to display the practicality and robustness the suggested scheme. The obtained numerical results have been illustrated with tables. Furthermore, to show the numerical behavior of the single soliton, some of the simulations are depicted in 2D and 3D. Present results show that the method procures high accurate solutions so present scheme will be useful for the other nonlinear scientific problems. After that, bifurcation behavior of traveling waves for the S-K equation has been examined depending on the velocity (v) of the traveling wave. It has been seen that velocity (v) of the traveling wave plays a key role for the existence of different kind of quasiperiodic motions of the nonlinear S-K equation. Coexisting quasiperiodic motions for traveling wave solutions of the equation have been presented.

Suggested Citation

  • Karakoc, Seydi Battal Gazi & Saha, Asit & Sucu, Derya Yıldırım, 2023. "A collocation algorithm based on septic B-splines and bifurcation of traveling waves for Sawada–Kotera equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 12-27.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:12-27
    DOI: 10.1016/j.matcom.2022.06.020
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    References listed on IDEAS

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    1. Djennadi, Smina & Shawagfeh, Nabil & Abu Arqub, Omar, 2021. "A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Shazalina Mat Zin & Ahmad Abd Majid & Ahmad Izani Md. Ismail & Muhammad Abbas, 2014. "Application of Hybrid Cubic B-Spline Collocation Approach for Solving a Generalized Nonlinear Klien-Gordon Equation," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-10, December.
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