IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v185y2021icp733-753.html
   My bibliography  Save this article

An almost second order hybrid scheme for the numerical solution of singularly perturbed parabolic turning point problem with interior layer

Author

Listed:
  • Yadav, Swati
  • Rai, Pratima

Abstract

In this article, we consider a one dimensional singularly perturbed parabolic convection–diffusion problem with interior turning point. The convection coefficient of the considered problem is vanishing inside the spatial domain and also, exhibits an interior layer. As a result, the exact solution of the considered problem contains an interior layer. A higher order numerical method is constructed and analyzed for the numerical solution of the considered problem. To discretize the time direction, we have used the classical implicit Euler method on a uniform mesh. Also, a hybrid finite difference scheme is employed on a generalized Shishkin mesh condensing in the interior layer region to discretize the spatial domain. Rigorous analysis is performed to show that the proposed method is ε-uniformly convergent of order almost two. The higher accuracy and convergence rate of the proposed scheme are verified via implementing numerical experiments on two test problems. Comparison is done with the scheme proposed in O’Riordan and Quinn (2015) for the considered class of problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:733-753
    DOI: 10.1016/j.matcom.2021.01.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421000343
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.01.017?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. 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.
    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)

    Citations

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


    Cited by:

    1. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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:185:y:2021:i:c:p:733-753. 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.