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A Modified Three-Level Average Linear-Implicit Finite Difference Method for the Rosenau-Burgers Equation

Author

Listed:
  • Jiraporn Janwised
  • Ben Wongsaijai
  • Thanasak Mouktonglang
  • Kanyuta Poochinapan

Abstract

We introduce a new technique, a three-level average linear-implicit finite difference method, for solving the Rosenau-Burgers equation. A second-order accuracy on both space and time numerical solution of the Rosenau-Burgers equation is obtained using a five-point stencil. We prove the existence and uniqueness of the numerical solution. Moreover, the convergence and stability of the numerical solution are also shown. The numerical results show that our method improves the accuracy of the solution significantly.

Suggested Citation

  • Jiraporn Janwised & Ben Wongsaijai & Thanasak Mouktonglang & Kanyuta Poochinapan, 2014. "A Modified Three-Level Average Linear-Implicit Finite Difference Method for the Rosenau-Burgers Equation," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-11, April.
    • Handle: RePEc:hin:jnlamp:734067
    DOI: 10.1155/2014/734067
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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. 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. 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).
    4. Hamid Ghadiri & Hamed Khodadadi & Saleh Mobayen & Jihad H. Asad & Thaned Rojsiraphisal & Arthur Chang, 2021. "Observer-Based Robust Control Method for Switched Neutral Systems in the Presence of Interval Time-Varying Delays," Mathematics, MDPI, vol. 9(19), pages 1-20, October.

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