IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v55y2024i4d10.1007_s13226-023-00445-8.html
   My bibliography  Save this article

An efficient numerical approximation for mixed singularly perturbed parabolic problems involving large time-lag

Author

Listed:
  • Sushree Priyadarshana

    (National Institute of Technology Rourkela)

  • Jugal Mohapatra

    (National Institute of Technology Rourkela)

Abstract

The objective of this work is to provide an efficient numerical scheme for solving singularly perturbed parabolic convection-diffusion problems with a large time lag having Robin-type boundary conditions. The implicit Euler scheme is used in the temporal direction on a uniform mesh. To handle the layer behavior caused due to the presence of perturbation parameter, the problem is solved using the upwind scheme on two layer-resolving meshes in the spatial direction. As the Shishkin mesh makes the order of convergence to one up to a logarithmic factor, in the spatial direction, the presence of this effect is prevented by the use of the Bakhvalov-Shishkin mesh. Further, the robustness of the scheme is tested over semi-linear time-lagged initial boundary value problems. Numerical outputs are presented in the form of tables and graphs to prove the parameter-uniform nature and robustness of the proposed scheme.

Suggested Citation

  • Sushree Priyadarshana & Jugal Mohapatra, 2024. "An efficient numerical approximation for mixed singularly perturbed parabolic problems involving large time-lag," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(4), pages 1389-1408, December.
  • Handle: RePEc:spr:indpam:v:55:y:2024:i:4:d:10.1007_s13226-023-00445-8
    DOI: 10.1007/s13226-023-00445-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-023-00445-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13226-023-00445-8?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. Das, Abhishek & Natesan, Srinivasan, 2015. "Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 168-186.
    2. Gowrisankar, S. & Natesan, Srinivasan, 2019. "An efficient robust numerical method for singularly perturbed Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 385-394.
    3. Avudai Selvi, P. & Ramanujam, N., 2017. "A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 101-115.
    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. Priyadarshana, S. & Mohapatra, J. & Pattanaik, S.R., 2023. "An improved time accurate numerical estimation for singularly perturbed semilinear parabolic differential equations with small space shifts and a large time lag," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 183-203.
    2. Cengizci, Süleyman & Uğur, Ömür, 2023. "A stabilized FEM formulation with discontinuity-capturing for solving Burgers’-type equations at high Reynolds numbers," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    3. Chen, Shu-Bo & Soradi-Zeid, Samaneh & Dutta, Hemen & Mesrizadeh, Mehdi & Jahanshahi, Hadi & Chu, Yu-Ming, 2021. "Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Kumar, Sunil & Sumit, & Ramos, Higinio, 2021. "Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. Yasir Nawaz & Muhammad Shoaib Arif & Wasfi Shatanawi & Amna Nazeer, 2021. "An Explicit Fourth-Order Compact Numerical Scheme for Heat Transfer of Boundary Layer Flow," Energies, MDPI, vol. 14(12), pages 1-17, June.

    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:spr:indpam:v:55:y:2024:i:4:d:10.1007_s13226-023-00445-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.