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Modified quintic trigonometric B-spline differential quadrature method for the improved Boussinesq equation

Author

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  • Deng, Jiawen
  • Hussain, Shahid
  • Rahman, Kaysar

Abstract

This study proposed a modified quintic trigonometric B-spline function applied within a differential quadrature method to solve the Improved Boussinesq equation, a key model for shallow water waves and nonlinear wave phenomena. Stability is analyzed through eigenvalue plots. The proposed technique successfully simulates both single and double solitary wave solutions, with results validated against established numerical methods and exact solutions, confirming its effectiveness. Additionally, the study explores physical phenomena such as Solitary wave splitting motion, interactions of double solitary waves, and mutual motion of multiple solitary waves. The findings highlight the method’s effectiveness in capturing the complex behaviors of solitary waves, serving as a valuable tool for research in nonlinear wave dynamics.

Suggested Citation

  • Deng, Jiawen & Hussain, Shahid & Rahman, Kaysar, 2025. "Modified quintic trigonometric B-spline differential quadrature method for the improved Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925012718
    DOI: 10.1016/j.chaos.2025.117258
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    References listed on IDEAS

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    1. Kaur, Navneet & Joshi, Varun, 2024. "Kuramoto-Sivashinsky equation: Numerical solution using two quintic B-splines and differential quadrature method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 105-127.
    2. Geeta Arora & Shubham Mishra & Homan Emaifar & Masoumeh Khademi & Mehmet Emir Koksal, 2023. "Numerical Simulation and Dynamics of Burgers’ Equation Using the Modified Cubic B-Spline Differential Quadrature Method," Discrete Dynamics in Nature and Society, Hindawi, vol. 2023, pages 1-8, March.
    3. Bratsos, A.G., 2009. "A predictor–corrector scheme for the improved Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2083-2094.
    4. Ucar, Y. & Karaagac, B. & Esen, A., 2015. "A new approach on numerical solutions of the Improved Boussinesq type equation using quadratic B-spline Galerkin finite element method," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 148-155.
    5. Mittal, R.C. & Dahiya, Sumita, 2017. "Numerical simulation of three-dimensional telegraphic equation using cubic B-spline differential quadrature method," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 442-452.
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