IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v281y2016icp356-380.html
   My bibliography  Save this article

Some high order difference schemes for the space and time fractional Bloch–Torrey equations

Author

Listed:
  • Sun, Hong
  • Sun, Zhi-zhong
  • Gao, Guang-hua

Abstract

In this paper, several difference schemes are proposed for both one-dimensional and two-dimensional space and time fractional Bloch–Torrey equations. The spatial second-order scheme and the spatial fourth-order compact scheme are established, respectively. The obtained schemes can achieve the global second-order numerical accuracy in time. The unique solvability, unconditional stability and convergence of the proposed schemes are proved by the energy method. Two ADI schemes are also discussed for the two dimensional problem. Numerical examples are given to verify the numerical accuracy and efficiency of the difference schemes.

Suggested Citation

  • Sun, Hong & Sun, Zhi-zhong & Gao, Guang-hua, 2016. "Some high order difference schemes for the space and time fractional Bloch–Torrey equations," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 356-380.
  • Handle: RePEc:eee:apmaco:v:281:y:2016:i:c:p:356-380
    DOI: 10.1016/j.amc.2016.01.044
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316300443
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2016.01.044?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. Zhao, Yong-Liang & Zhu, Pei-Yong & Luo, Wei-Hua, 2018. "A fast second-order implicit scheme for non-linear time-space fractional diffusion equation with time delay and drift term," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 231-248.
    2. Zhang, Qifeng & Ren, Yunzhu & Lin, Xiaoman & Xu, Yinghong, 2019. "Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 91-110.
    3. Zhang, Xue & Gu, Xian-Ming & Zhao, Yong-Liang & Li, Hu & Gu, Chuan-Yun, 2024. "Two fast and unconditionally stable finite difference methods for Riesz fractional diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    4. Tan, Zhijun & Zeng, Yunhua, 2024. "Temporal second-order fully discrete two-grid methods for nonlinear time-fractional variable coefficient diffusion-wave equations," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    5. Bu, Weiping & Zhao, Yanmin & Shen, Chen, 2021. "Fast and efficient finite difference/finite element method for the two-dimensional multi-term time-space fractional Bloch-Torrey equation," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    6. Wang, Jinfeng & Yin, Baoli & Liu, Yang & Li, Hong & Fang, Zhichao, 2021. "Mixed finite element algorithm for a nonlinear time fractional wave model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 60-76.

    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:281:y:2016:i:c:p:356-380. 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.