IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v361y2019icp752-765.html
   My bibliography  Save this article

A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation

Author

Listed:
  • Shen, Jinye
  • Sun, Zhi-zhong
  • Cao, Wanrong

Abstract

In this paper, a finite difference scheme for time-fractional nonlinear Korteweg-de Vries (KdV) problems with the Caputo-type fractional derivative is presented. To deal with the weak singularity caused by the fractional derivative that the solution has in the initial layer, the well-known L1 scheme on graded meshes has been used for time discretization. Meanwhile, a nonlinear finite difference approximation on uniform meshes is proposed for spatial discretization. The existence, stability and convergence of the numerical solution are studied by the energy method. It is proved that the scheme is of min{2−α,rα} order convergence in time and of first-order convergence in space, where α is the order of fractional derivative and r is a parameter of graded meshes. Furthermore, in order to increase computational efficiency, the corresponding fast algorithm of the presented scheme has been considered. In numerical simulation, a valid approach based on linear interpolation is designed to test convergence rate for the scheme on temporal graded meshes. Numerical results demonstrate sharpness of the theoretical convergence estimate and effectiveness of the fast algorithm.

Suggested Citation

  • Shen, Jinye & Sun, Zhi-zhong & Cao, Wanrong, 2019. "A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 752-765.
  • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:752-765
    DOI: 10.1016/j.amc.2019.06.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319304886
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2019.06.023?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Changpin & Wang, Zhen, 2021. "Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 838-857.
    2. Yousif, Majeed A. & Hamasalh, Faraidun K., 2024. "The fractional non-polynomial spline method: Precision and modeling improvements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 512-525.

    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:361:y:2019:i:c:p:752-765. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.