IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v228y2025icp245-262.html
   My bibliography  Save this article

An exponential spectral deferred correction method for multidimensional parabolic problems

Author

Listed:
  • Wang, Yurun
  • Liu, Fei

Abstract

We present some efficient algorithms based on an exponential time differencing spectral deferred correction (ETDSDC) method for multidimensional second and fourth-order parabolic problems with non-periodic boundary conditions including Dirichlet, Neumann, Robin boundary conditions. Similar to the Fourier spectral method for periodic problems, the key to the efficiency of our algorithms is to construct diagonal discrete linear operators via Legendre–Galerkin methods with Fourier-like basis functions. In combination with the ETDSDC scheme, the proposed methods are spectrally accurate in space and up to 10th-order accurate in time (as shown in this work). We demonstrate the high-order of convergence and efficiency of our algorithms in solving parabolic equations through a series of two-dimensional and three-dimensional examples including Ginzburg–Landau and Allen–Cahn equations.

Suggested Citation

  • Wang, Yurun & Liu, Fei, 2025. "An exponential spectral deferred correction method for multidimensional parabolic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 245-262.
  • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:245-262
    DOI: 10.1016/j.matcom.2024.09.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424003495
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2024.09.003?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. Yongho Kim & Gilnam Ryu & Yongho Choi, 2021. "Fast and Accurate Numerical Solution of Allen–Cahn Equation," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-12, December.
    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. Yang, Junxiang & Lee, Dongsun & Kwak, Soobin & Ham, Seokjun & Kim, Junseok, 2024. "The Allen–Cahn model with a time-dependent parameter for motion by mean curvature up to the singularity," Chaos, Solitons & Fractals, Elsevier, vol. 182(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:228:y:2025:i:c:p:245-262. 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.