IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v192y2022icp201-220.html
   My bibliography  Save this article

Collocation method using artificial viscosity for time dependent singularly perturbed differential–difference equations

Author

Listed:
  • Daba, Imiru Takele
  • Duressa, Gemechis File

Abstract

A parameter uniform numerical method is presented for solving singularly perturbed time-dependent differential–difference equations with small shifts. To approximate the terms with the shifts, Taylor’s series expansion is used. The resulting singularly perturbed parabolic partial differential equation is solved using an implicit Euler method in temporal direction and cubic B-spline collocation method for the resulting system of ordinary differential equations in spatial direction, and an artificial viscosity is introduced in the scheme using the theory of singular perturbations. The proposed method is shown to be accurate of order OΔt+h2 by preserving ɛ-uniform convergence, where h and Δt denote spatial and temporal step sizes, respectively. Several test examples are solved to demonstrate the effectiveness of the proposed method. The computed numerical results show that the proposed method provides more accurate results than some methods exist in the literature and suitable for solving such problems with little computational effort.

Suggested Citation

  • Daba, Imiru Takele & Duressa, Gemechis File, 2022. "Collocation method using artificial viscosity for time dependent singularly perturbed differential–difference equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 201-220.
    • Handle: RePEc:eee:matcom:v:192:y:2022:i:c:p:201-220
    DOI: 10.1016/j.matcom.2021.09.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421003207
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.09.005?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. 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.
    2. Gemechis File Duressa & Imiru Takele Daba & Chernet Tuge Deressa, 2023. "A Systematic Review on the Solution Methodology of Singularly Perturbed Differential Difference Equations," Mathematics, MDPI, vol. 11(5), pages 1-16, February.

    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:192:y:2022:i:c:p:201-220. 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.