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A reduced high-order compact finite difference scheme based on proper orthogonal decomposition technique for KdV equation

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  • Zhang, Xiaohua
  • Zhang, Ping

Abstract

In this paper, a reduced implicit sixth-order compact finite difference (CFD6) scheme which combines proper orthogonal decomposition (POD) technique and high-order compact finite difference scheme is presented for numerical solution of the Korteweg-de Vries (KdV) equation. High-order compact finite difference scheme is applied to attain high accuracy for KdV equation and the POD technique is used to improve the computational efficiency of the high-order compact finite difference scheme. This method is validated by considering the simulation of five examples, and the numerical results demonstrate that the reduced sixth-order compact finite difference (R-CFD6) scheme can largely improve the computational efficiency without a significant loss in accuracy for solving KdV equation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:535-545
    DOI: 10.1016/j.amc.2018.07.017
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    References listed on IDEAS

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    1. 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.
    2. Skogestad, Jan Ole & Kalisch, Henrik, 2009. "A boundary value problem for the KdV equation: Comparison of finite-difference and Chebyshev methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 151-163.
    3. Yan, Guangwu & Zhang, Jianying, 2009. "A higher-order moment method of the lattice Boltzmann model for the Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1554-1565.
    4. El-Zoheiry, H. & Iskandar, L. & El-Naggar, B., 1994. "The Quintic spline for solving the Korteweg-de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 37(6), pages 539-549.
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