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A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation

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  • Jinsong Hu
  • Yulan Wang

Abstract

We study the initial-boundary value problem for Rosenau-RLW equation. We propose a three-level linear finite difference scheme, which has the theoretical accuracy of . The scheme simulates two conservative properties of original problem well. The existence, uniqueness of difference solution, and a priori estimates in infinite norm are obtained. Furthermore, we analyze the convergence and stability of the scheme by energy method. At last, numerical experiments demonstrate the theoretical results.

Suggested Citation

  • Jinsong Hu & Yulan Wang, 2013. "A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, November.
    • Handle: RePEc:hin:jnlmpe:870291
    DOI: 10.1155/2013/870291
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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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