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Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation

Author

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  • Wongsaijai, B.
  • Mouktonglang, T.
  • Sukantamala, N.
  • Poochinapan, K.

Abstract

A mass-preserving scheme, a nonlinear algorithm based on modification of a finite difference method to the Rosenau-RLW equation, is proposed subject to homogeneous boundary conditions. The key feature of the method for improving the accuracy of approximate solutions is to develop a compact higher-order scheme together with an iterative algorithm for solving the nonlinear implicit scheme. The derivatives for space discretization are approximated by using the algorithm dealing with a five-point stencil. In addition, a three-level average difference technique is used to perform time discretization. The conservation of mass and both the existence and uniqueness of the numerical solution are proved. The stability and convergence of the numerical solution with order O(τ4+τ2h2+h4) are also confirmed. For efficiency analysis, numerical results show that the computational efficiency of the compact scheme is much higher than that of non-compact schemes. Moreover, long-time behavior is also used to validate the capability of the present method.

Suggested Citation

  • Wongsaijai, B. & Mouktonglang, T. & Sukantamala, N. & Poochinapan, K., 2019. "Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 84-100.
    • Handle: RePEc:eee:apmaco:v:340:y:2019:i:c:p:84-100
    DOI: 10.1016/j.amc.2018.06.009
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    Cited by:

    1. Wongsaijai, B. & Oonariya, C. & Poochinapan, K., 2020. "Compact structure-preserving algorithm with high accuracy extended to the improved Boussinesq equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 125-150.
    2. 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).
    3. Mouktonglang, Thanasak & Yimnet, Suriyon & Sukantamala, Nattakorn & Wongsaijai, Ben, 2022. "Dynamical behaviors of the solution to a periodic initial–boundary value problem of the generalized Rosenau-RLW-Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 114-136.
    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. 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.
    6. Poochinapan, Kanyuta & Wongsaijai, Ben, 2022. "Numerical analysis for solving Allen-Cahn equation in 1D and 2D based on higher-order compact structure-preserving difference scheme," Applied Mathematics and Computation, Elsevier, vol. 434(C).

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