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A high-order combined finite element/interpolation approach for multidimensional nonlinear generalized Benjamin–Bona–Mahony–Burgers equation

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  • Ngondiep, Eric

Abstract

A high-order combined finite element/interpolation approach is developed for solving a multidimensional nonlinear generalized Benjamin–Bona–Mahony–Burgers equation subjected to suitable initial and boundary conditions. In the proposed high-order scheme we approximate the time derivative with piecewise polynomial interpolation of second-order and use the finite element discretization of piecewise polynomials of degree q and q+1, where q≥2 is an integer, to approximating the space derivatives. The stability together with the error estimates of the constructed technique are established in W21(Ω)-norm. The analysis suggests that the developed numerical scheme is unconditionally stable, temporal second-order accurate and convergence in space with order q. Furthermore, the new procedure is faster and more efficient than a broad range of numerical methods discussed in the literature for the given initial–boundary value problem. A wide set of examples are performed to confirming the theoretical studies.

Suggested Citation

  • Ngondiep, Eric, 2024. "A high-order combined finite element/interpolation approach for multidimensional nonlinear generalized Benjamin–Bona–Mahony–Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 560-577.
    • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:560-577
    DOI: 10.1016/j.matcom.2023.08.041
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    References listed on IDEAS

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    1. Li, Lingfei & Xie, Yingying, 2021. "Rogue wave solutions of the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Hajishafieiha, J. & Abbasbandy, S., 2020. "A new class of polynomial functions for approximate solution of generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equations," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    3. S. Kutluay & A. Esen, 2006. "A finite difference solution of the regularized long-wave equation," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-14, March.
    4. Xie, Yingying & Li, Lingfei, 2022. "Multiple-order breathers for a generalized (3+1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation near the offshore structure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 19-31.
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