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A reduced-order extrapolation central difference scheme based on POD for two-dimensional fourth-order hyperbolic equations

Author

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  • Luo, Zhendong
  • Jin, Shiju
  • Chen, Jing

Abstract

This paper is concerned with establishing the reduced-order extrapolation central difference (ROECD) scheme based on proper orthogonal decomposition (POD) for two-dimensional (2D) fourth-order hyperbolic equations. For this purpose, we first develop the classical central difference (CD) scheme for the 2D fourth-order hyperbolic equations and analyze its stability and convergence. Then by making use of the POD method, we build the ROECD scheme with fewer degrees of freedom and sufficiently high accuracy and furnish the error estimates of the ROECD solutions and the algorithm procedure for solving the ROECD scheme. Finally, we employ some numerical examples to confirm the correctness of theoretical conclusions. This implies that ROECD scheme is feasible and efficient for seeking the numerical solutions of the 2D fourth-order hyperbolic equations.

Suggested Citation

  • Luo, Zhendong & Jin, Shiju & Chen, Jing, 2016. "A reduced-order extrapolation central difference scheme based on POD for two-dimensional fourth-order hyperbolic equations," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 396-408.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:396-408
    DOI: 10.1016/j.amc.2016.05.032
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    References listed on IDEAS

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    1. K. Kunisch & S. Volkwein, 1999. "Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 345-371, August.
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    Cited by:

    1. Zhang, Xiaohua & Zhang, Ping, 2018. "A reduced high-order compact finite difference scheme based on proper orthogonal decomposition technique for KdV equation," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 535-545.
    2. Luo, Zhendong & Teng, Fei, 2018. "A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 374-383.
    3. Zeng, Yihui & Luo, Zhendong, 2022. "The Crank–Nicolson mixed finite element method for the improved system of time-domain Maxwell’s equations," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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