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Direct WENO scheme for dispersion-type equations

Author

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  • Ahmat, Muyassar
  • Qiu, Jianxian

Abstract

In this paper, we present a weighted essentially non-oscillatory (WENO) scheme for dispersive equations which may generate physical high-frequency oscillation in the non-smooth interface. The third derivative term is approximated directly by a conservative flux difference. A finite-difference WENO scheme of fifth-order is constructed for the discretization of spatial differentiation. The wave behavior of linear and nonlinear dispersion equations is simulated by using the proposed scheme in space direction and the third-order TVD Runge–Kutta method in the time direction. Numerical examples demonstrate the accuracy and good performance of the proposed scheme.

Suggested Citation

  • Ahmat, Muyassar & Qiu, Jianxian, 2023. "Direct WENO scheme for dispersion-type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 216-229.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:216-229
    DOI: 10.1016/j.matcom.2022.08.010
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    References listed on IDEAS

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    1. Ismail, M.S. & Taha, T.R., 1998. "A numerical study of compactons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(6), pages 519-530.
    2. Rathan, Samala & Kumar, Rakesh & Jagtap, Ameya D., 2020. "L1-type smoothness indicators based WENO scheme for nonlinear degenerate parabolic equations," Applied Mathematics and Computation, Elsevier, vol. 375(C).
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