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Numerical Simulation for General Rosenau-RLW Equation: An Average Linearized Conservative Scheme

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  • Xintian Pan
  • Luming Zhang

Abstract

Numerical solutions for the general Rosenau-RLW equation are considered and an energy conservative linearized finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence, and a priori error estimate of the scheme are proved using energy method. Numerical results demonstrate that the scheme is efficient and reliable.

Suggested Citation

  • Xintian Pan & Luming Zhang, 2012. "Numerical Simulation for General Rosenau-RLW Equation: An Average Linearized Conservative Scheme," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-15, May.
    • Handle: RePEc:hin:jnlmpe:517818
    DOI: 10.1155/2012/517818
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    Cited by:

    1. Zakieh Avazzadeh & Omid Nikan & José A. Tenreiro Machado, 2020. "Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    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. 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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