IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v264y2015icp378-391.html
   My bibliography  Save this article

Time-dependent Hermite–Galerkin spectral method and its applications

Author

Listed:
  • Luo, Xue
  • Yau, Shing-Tung
  • Yau, Stephen S.-T.

Abstract

A time-dependent Hermite–Galerkin spectral method (THGSM) is investigated in this paper for the nonlinear convection–diffusion equations in the unbounded domains. The time-dependent scaling factor and translating factor are introduced in the definition of the generalized Hermite functions (GHF). As a consequence, the THGSM based on these GHF has many advantages, not only in theoretical proofs, but also in numerical implementations. The stability and spectral convergence of our proposed method have been established in this paper. The Korteweg–de Vries–Burgers (KdVB) equation and its special cases, including the heat equation and the Burgers’ equation, as the examples, have been numerically solved by our method. The numerical results are presented, and it surpasses the existing methods in accuracy. Our theoretical proof of the spectral convergence has been supported by the numerical results.

Suggested Citation

  • Luo, Xue & Yau, Shing-Tung & Yau, Stephen S.-T., 2015. "Time-dependent Hermite–Galerkin spectral method and its applications," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 378-391.
    • Handle: RePEc:eee:apmaco:v:264:y:2015:i:c:p:378-391
    DOI: 10.1016/j.amc.2015.04.088
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315005500
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.04.088?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.

    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:264:y:2015:i:c:p:378-391. 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.