IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v194y2022icp329-347.html
   My bibliography  Save this article

Fast ADI difference/compact difference schemes for the nonlocal evolution equation with weakly singular kernels in three dimensions

Author

Listed:
  • Qiao, Leijie
  • Xu, Da
  • Tang, Bo
  • Zhou, Jun

Abstract

We consider two kinds of efficient numerical methods to solve the three-dimensional evolution equation with weakly singular kernels. The proposed techniques are based on the finite difference/compact difference methods for the spatial discretization and an alternating direction implicit (ADI) algorithm for the time direction, combined with the second-order convolution quadrature (CQ) rule for the Riemann–Liouville (R-L) integral term and the classical L1 formula for the Caputo fractional derivative. The unconditional stability and convergence of the ADI finite difference scheme are proved rigorously. Numerical results are presented to support the theoretical analysis.

Suggested Citation

  • Qiao, Leijie & Xu, Da & Tang, Bo & Zhou, Jun, 2022. "Fast ADI difference/compact difference schemes for the nonlocal evolution equation with weakly singular kernels in three dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 329-347.
  • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:329-347
    DOI: 10.1016/j.matcom.2021.12.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421004390
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2021.12.005?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. Qiao, Leijie & Xu, Da & Wang, Zhibo, 2019. "An ADI difference scheme based on fractional trapezoidal rule for fractional integro-differential equation with a weakly singular kernel," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 103-114.
    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. Fang, Xing & Qiao, Leijie & Zhang, Fengyang & Sun, Fuming, 2023. "Explore deep network for a class of fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

    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:matcom:v:194:y:2022:i:c:p:329-347. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.