IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v211y2023icp192-213.html
   My bibliography  Save this article

An almost second-order robust computational technique for singularly perturbed parabolic turning point problem with an interior layer

Author

Listed:
  • Sahoo, Sanjay Ku
  • Gupta, Vikas

Abstract

The subject of this paper is the numerical investigation of a singularly perturbed parabolic problem with a simple interior turning point on a rectangular domain in the x−t plane with Dirichlet boundary conditions. At the location of the turning point, the solution to this class of problems has an internal layer. By decomposing the solution into a regular and singular component, we may first establish stronger bounds for the regular and singular components, as well as their derivatives. The fitted mesh finite difference scheme, which consists of a hybrid finite difference operator on a non-uniform Shishkin mesh in the space direction and a backward implicit Euler scheme on a uniform mesh in the time variable, is used to identify the approximate numerical solution. The accuracy of the resulting scheme is then improved in the temporal direction using the Richardson extrapolation scheme, which reveals that the extrapolated scheme is almost second-order uniformly convergent in both space and time variables when ɛ≤CN−1. Two numerical examples are used to demonstrate the efficacy and accuracy of the finite difference approaches mentioned.

Suggested Citation

  • Sahoo, Sanjay Ku & Gupta, Vikas, 2023. "An almost second-order robust computational technique for singularly perturbed parabolic turning point problem with an interior layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 192-213.
    • Handle: RePEc:eee:matcom:v:211:y:2023:i:c:p:192-213
    DOI: 10.1016/j.matcom.2023.04.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423001660
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.04.012?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. 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.
    2. Yadav, Swati & Rai, Pratima, 2020. "A higher order numerical scheme for singularly perturbed parabolic turning point problems exhibiting twin boundary layers," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    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. 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.
    2. Yadav, Swati & Rai, Pratima, 2023. "A parameter uniform higher order scheme for 2D singularly perturbed parabolic convection–diffusion problem with turning point," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 507-531.

    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:211:y:2023:i:c:p:192-213. 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.