IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v313y2017icp453-473.html
   My bibliography  Save this article

Alternating direction numerical scheme for singularly perturbed 2D degenerate parabolic convection-diffusion problems

Author

Listed:
  • Majumdar, Anirban
  • Natesan, Srinivasan

Abstract

In this article, we study the numerical solution of singularly perturbed 2D degenerate parabolic convection-diffusion problems on a rectangular domain. The solution of this problem exhibits parabolic boundary layers along x=0,y=0 and a corner layer in the neighborhood of (0, 0). First, we use an alternating direction implicit finite difference scheme to discretize the time derivative of the continuous problem on a uniform mesh in the temporal direction. Then, to discretize the spatial derivatives of the resulting time semidiscrete problems, we apply the upwind finite difference scheme on a piecewise-uniform Shishkin mesh. We derive error estimate for the proposed numerical scheme, which shows that the scheme is ε-uniformly convergent of almost first-order (up to a logarithmic factor) in space and first-order in time. Some numerical results have been carried out to validate the theoretical results.

Suggested Citation

  • Majumdar, Anirban & Natesan, Srinivasan, 2017. "Alternating direction numerical scheme for singularly perturbed 2D degenerate parabolic convection-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 453-473.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:453-473
    DOI: 10.1016/j.amc.2017.06.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317304228
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.06.010?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.

    References listed on IDEAS

    as
    1. S. Natesan & M. Ramanujam, 1998. "Initial-Value Technique for Singularly-Perturbed Turning-Point Problems Exhibiting Twin Boundary Layers," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 37-52, October.
    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. 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.

    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. T. Valanarasu & N. Ramanujam, 2007. "Asymptotic Initial-Value Method for Second-Order Singular Perturbation Problems of Reaction-Diffusion Type with Discontinuous Source Term," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 371-383, June.
    2. Singh, Satpal & Kumar, Devendra & Ramos, Higinio, 2022. "A uniformly convergent quadratic B-spline based scheme for singularly perturbed degenerate parabolic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 88-106.
    3. T. Valanarasu & N. Ramanujan, 2003. "Asymptotic Initial-Value Method for Singularly-Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 167-182, January.

    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:313:y:2017:i:c:p:453-473. 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.