IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v160y2019icp155-167.html
   My bibliography  Save this article

A robust fitted operator finite difference method for singularly perturbed problems whose solution has an interior layer

Author

Listed:
  • Munyakazi, Justin B.
  • Patidar, Kailash C.
  • Sayi, Mbani T.

Abstract

The objectives of this paper are to construct and study a fitted operator finite difference method for the class of singularly perturbed problems whose solution exhibits an interior layer due to the presence of a turning point. We first establish sharp bounds on the solution and its derivatives. Then in line with other fitted operator methods that are designed in various recent works in numerical singular perturbation theory by the first two authors, we propose a fitted operator finite difference method to solve this interior layer problem. This method is then analysed by making use of the bounds on the solutions that we derive. We show that the scheme is uniformly convergent of order one. We also apply Richardson extrapolation as the acceleration technique to improve the accuracy and the order of convergence of the scheme up to two. Numerical investigations are carried out to demonstrate the efficacy and robustness of the scheme.

Suggested Citation

  • Munyakazi, Justin B. & Patidar, Kailash C. & Sayi, Mbani T., 2019. "A robust fitted operator finite difference method for singularly perturbed problems whose solution has an interior layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 155-167.
    • Handle: RePEc:eee:matcom:v:160:y:2019:i:c:p:155-167
    DOI: 10.1016/j.matcom.2018.12.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847541830329X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2018.12.010?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.

    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. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    3. Kumar, Sunil & Sumit, & Vigo-Aguiar, Jesus, 2022. "A high order convergent numerical method for singularly perturbed time dependent problems using mesh equidistribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 287-306.
    4. Yadav, Swati & Rai, Pratima, 2021. "An almost second order hybrid scheme for the numerical solution of singularly perturbed parabolic turning point problem with interior layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 733-753.

    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:160:y:2019:i:c:p:155-167. 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: 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.