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Asymptotic Analysis and Error Estimate for Rosenau-Burgers Equation

Author

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  • Jun Zhang
  • Zixin Liu
  • Fubiao Lin
  • Jianjun Jiao

Abstract

In this work, the asymptotic stability result for Rosenau-Burgers equation is established, under appropriate assumptions on steady state eigenvalue problem and the forcing function. In addition, we propose and analyze a linearized numerical method for solving this nonlinear Rosenau-Burgers equation. We prove that the numerical scheme is unconditionally stable, and the error estimate shows that the numerical method is in the order of , where , , and are, respectively, step of time, polynomial degree, and regularity of . Numerical examples are illustrated to verify the theoretical results.

Suggested Citation

  • Jun Zhang & Zixin Liu & Fubiao Lin & Jianjun Jiao, 2019. "Asymptotic Analysis and Error Estimate for Rosenau-Burgers Equation," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, June.
    • Handle: RePEc:hin:jnlmpe:9673514
    DOI: 10.1155/2019/9673514
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    Cited by:

    1. 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.
    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).

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