IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v431y2022ics0096300322004192.html
   My bibliography  Save this article

Convergence analysis of Jacobi spectral collocation methods for weakly singular nonlocal diffusion equations with volume constraints

Author

Listed:
  • Lu, Jiashu
  • Yang, Mengna
  • Nie, Yufeng

Abstract

This paper considers efficient spectral solutions for weakly singular nonlocal diffusion equations with Dirichlet-type volume constraints. The equation we consider contains an integral operator that typically has a singularity at the midpoint of the integral domain, and the approximation of the integral operator is one of the essential difficulties in solving nonlocal equations. To overcome this problem, two-sided Jacobi spectral quadrature rules are proposed to develop a Jacobi spectral collocation method for nonlocal diffusion equations. A rigorous convergence analysis of the proposed method with the L∞ norm is presented, and we further prove that the Jacobi collocation solution converges to its corresponding local limit as nonlocal interactions vanish. Numerical examples are given to verify the theoretical results.

Suggested Citation

  • Lu, Jiashu & Yang, Mengna & Nie, Yufeng, 2022. "Convergence analysis of Jacobi spectral collocation methods for weakly singular nonlocal diffusion equations with volume constraints," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322004192
    DOI: 10.1016/j.amc.2022.127345
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322004192
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127345?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. Tian, Hao & Zhang, Jing & Ju, Lili, 2020. "A spectral collocation method for nonlocal diffusion equations with volume constrained boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    2. Sohrabi, S. & Ranjbar, H. & Saei, M., 2017. "Convergence analysis of the Jacobi-collocation method for nonlinear weakly singular Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 141-152.
    3. Yao, Guoqing & Tao, DongYa & Zhang, Chao, 2022. "A hybrid spectral method for the nonlinear Volterra integral equations with weakly singular kernel and vanishing delays," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    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. Yu, Hao & Wu, Boying & Zhang, Dazhi, 2018. "A generalized Laguerre spectral Petrov–Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 96-111.
    2. Ahmed Z. Amin & Mahmoud A. Zaky & Ahmed S. Hendy & Ishak Hashim & Ahmed Aldraiweesh, 2022. "High-Order Multivariate Spectral Algorithms for High-Dimensional Nonlinear Weakly Singular Integral Equations with Delay," Mathematics, MDPI, vol. 10(17), pages 1-20, August.

    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:431:y:2022:i:c:s0096300322004192. 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.