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Conservative finite difference scheme for the nonlinear fourth-order wave equation

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  • Achouri, Talha

Abstract

A conservative finite difference scheme is presented for solving the two-dimensional fourth-order nonlinear wave equation. The existence of the numerical solution of the finite difference scheme is proved by Brouwer fixed point theorem. With the aid of the fact that the discrete energy is conserved, the finite difference solution is proved to be bounded in the discrete L∞−norm. Then, the difference solution is shown to be second order convergent in the discrete L∞−norm. A numerical example shows the efficiency of the proposed scheme.

Suggested Citation

  • Achouri, Talha, 2019. "Conservative finite difference scheme for the nonlinear fourth-order wave equation," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 121-131.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:121-131
    DOI: 10.1016/j.amc.2019.04.033
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    References listed on IDEAS

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    1. Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2015. "Energy conservation issues in the numerical solution of the semilinear wave equation," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 842-870.
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    Cited by:

    1. Zhang, Gengen, 2021. "Two conservative and linearly-implicit compact difference schemes for the nonlinear fourth-order wave equation," Applied Mathematics and Computation, Elsevier, vol. 401(C).

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