IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v329y2018icp154-174.html
   My bibliography  Save this article

Solving singularly perturbed problems by a weak-form integral equation with exponential trial functions

Author

Listed:
  • Liu, Chein-Shan

Abstract

The second-order singularly perturbed problem is transformed to a singularly perturbed parabolic type partial differential equation by using a fictitious time technique. Then we use Green’s second identity to derive a boundary integral equation in terms of the adjoint Trefftz test functions, namely a weak-form integral equation method (WFIEM). It accompanying with the exponential trial functions, which are designed to satisfy the boundary conditions automatically, can provide very accurate numerical solutions of linear and nonlinear singularly perturbed problems. For the latter problem the iterative procedure is convergent very fast.

Suggested Citation

  • Liu, Chein-Shan, 2018. "Solving singularly perturbed problems by a weak-form integral equation with exponential trial functions," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 154-174.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:154-174
    DOI: 10.1016/j.amc.2018.02.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318300961
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.02.002?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. Chein-Shan Liu, 2012. "The Lie-Group Shooting Method for Solving Multi-dimensional Nonlinear Boundary Value Problems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 468-495, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Chein-Shan & Li, Botong, 2021. "Solving a singular beam equation by the method of energy boundary functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 419-435.
    2. Liu, Chein-Shan & Chang, Chih-Wen, 2022. "Modified asymptotic solutions for second-order nonlinear singularly perturbed boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 139-152.

    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. Liu, Chein-Shan & Chang, Chih-Wen, 2022. "Modified asymptotic solutions for second-order nonlinear singularly perturbed boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 139-152.

    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:329:y:2018:i:c:p:154-174. 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.