IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v339y2018icp535-545.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318305757
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2018.07.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Che Sidik, Nor Azwadi & Aisyah Razali, Siti, 2014. "Lattice Boltzmann method for convective heat transfer of nanofluids – A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 38(C), pages 864-875.
    2. Otomo, Hiroshi & Boghosian, Bruce M. & Dubois, François, 2017. "Two complementary lattice-Boltzmann-based analyses for nonlinear systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 1000-1011.
    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).
    4. Kohnesara, Sima Molaei & Firoozjaee, Ali Rahmani, 2023. "Numerical solution of Korteweg–de Vries equation using discrete least squares meshless method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 65-76.
    5. Krivovichev, Gerasim V., 2018. "Linear Bhatnagar–Gross–Krook equations for simulation of linear diffusion equation by lattice Boltzmann method," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 102-119.
    6. 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.
    7. Du, Rui & Sun, Dongke & Shi, Baochang & Chai, Zhenhua, 2019. "Lattice Boltzmann model for time sub-diffusion equation in Caputo sense," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 80-90.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:535-545. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.