IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v457y2023ics0096300323003764.html
   My bibliography  Save this article

Structural schemes for one dimension stationary equations

Author

Listed:
  • Clain, Stéphane
  • Pereira, Rui M.S.
  • Pereira, Paulo A.
  • Lopes, Diogo

Abstract

In this paper, we propose a new paradigm for finite differences numerical methods, based on compact schemes to provide high order accurate approximations of a smooth solution. The method involves its derivatives approximations at the grid points and the construction of structural equations deriving from the kernels of a matrix that gathers the variables belonging to a small stencil. Numerical schemes involve combinations of physical equations and the structural relations. We have analysed the spectral resolution of the most common structural equations and performed numerical tests to address both the stability and accuracy issues for popular linear and non-linear problems. Several benchmarks are presented that ensure that the developed technology can cope with several problems that may involve non-linearity.

Suggested Citation

  • Clain, Stéphane & Pereira, Rui M.S. & Pereira, Paulo A. & Lopes, Diogo, 2023. "Structural schemes for one dimension stationary equations," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    • Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003764
    DOI: 10.1016/j.amc.2023.128207
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323003764
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128207?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:457:y:2023:i:c:s0096300323003764. 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.