IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v102y2017icp361-371.html
   My bibliography  Save this article

Asymptotically compatible schemes for space-time nonlocal diffusion equations

Author

Listed:
  • Chen, An
  • Du, Qiang
  • Li, Changpin
  • Zhou, Zhi

Abstract

In this paper, we study a space-time nonlocal diffusion model that reduces to the classical diffusion equation in the local limit. Firstly, we show the uniqueness and existence of the weak solution of the nonlocal model, and study the local limit of the nonlocal model as horizon parameters approach zero. Particularly, it is shown that the convergence is uniform at a rate of O(δ+σ2), under certain regularity assumptions on initial and source data. Next we propose a fully discrete scheme, by exploiting the quadrature-based finite difference method in time and the Fourier spectral method in space, and show its stability. The numerical scheme is proved to be asymptotically compatible so that it preserves the local limiting behavior at the discrete level. Numerical experiments are provided to illustrate the theoretical results.

Suggested Citation

  • Chen, An & Du, Qiang & Li, Changpin & Zhou, Zhi, 2017. "Asymptotically compatible schemes for space-time nonlocal diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 361-371.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:361-371
    DOI: 10.1016/j.chaos.2017.03.061
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917301236
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.03.061?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. Chenkuan Li & Changpin Li & Thomas Humphries & Hunter Plowman, 2019. "Remarks on the Generalized Fractional Laplacian Operator," Mathematics, MDPI, vol. 7(4), pages 1-17, March.

    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:chsofr:v:102:y:2017:i:c:p:361-371. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.