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Numerical simulation of wave flow : Integrating the BBM-KdV equation using compact difference schemes

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  • Polwang, Apipoom
  • Poochinapan, Kanyuta
  • Wongsaijai, Ben

Abstract

The nonlinear convection term uux plays a critical role in scientific and engineering contexts, capturing the complex interaction between a function and its spatial derivative. In numerical analysis, this term significantly impacts the stability of computational methods and requires careful treatment for accurate solutions. This study presents efficient, high-order linear numerical schemes for solving the Benjamin–Bona–Mahony-KdV equation, incorporating three strategies to approximate the nonlinear term while preserving mass and/or energy. The effectiveness and precision of the proposed methods are demonstrated through rigorous testing in comprehensive numerical experiments, providing clear insight into their performance. Our observations show that these schemes preserve conservative properties while offering improved accuracy and stability compared to the standard second-order scheme. These findings underscore the potential to advance numerical methods for differential equations and provide strong evidence for the effectiveness of the proposed high-order approach in accurately modeling complex wave behavior.

Suggested Citation

  • Polwang, Apipoom & Poochinapan, Kanyuta & Wongsaijai, Ben, 2025. "Numerical simulation of wave flow : Integrating the BBM-KdV equation using compact difference schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 236(C), pages 70-89.
    • Handle: RePEc:eee:matcom:v:236:y:2025:i:c:p:70-89
    DOI: 10.1016/j.matcom.2025.03.012
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    References listed on IDEAS

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    1. Wang, Xiaofeng & Dai, Weizhong & Guo, Shuangbing, 2019. "A conservative linear difference scheme for the 2D regularized long-wave equation," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 55-70.
    2. Teeranush Suebcharoen & Kanyuta Poochinapan & Ben Wongsaijai, 2022. "Bifurcation Analysis and Numerical Study of Wave Solution for Initial-Boundary Value Problem of the KdV-BBM Equation," Mathematics, MDPI, vol. 10(20), pages 1-20, October.
    3. Peng, Xiangyi & Xu, Da & Qiu, Wenlin, 2023. "Pointwise error estimates of compact difference scheme for mixed-type time-fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 702-726.
    4. Poochinapan, Kanyuta & Wongsaijai, Ben, 2023. "High-performance computing of structure-preserving algorithm for the coupled BBM system formulated by weighted compact difference operators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 439-467.
    5. Wongsaijai, Ben & Poochinapan, Kanyuta, 2021. "Optimal decay rates of the dissipative shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation with power of nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    6. Rouatbi, Asma & Omrani, Khaled, 2017. "Two conservative difference schemes for a model of nonlinear dispersive equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 516-530.
    7. He, Dongdong & Pan, Kejia, 2015. "A linearly implicit conservative difference scheme for the generalized Rosenau–Kawahara-RLW equation," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 323-336.
    8. Dimitrienko, Yu.I. & Li, Shuguang & Niu, Yi, 2021. "Study on the dynamics of a nonlinear dispersion model in both 1D and 2D based on the fourth-order compact conservative difference scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 661-689.
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