IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v200y2022icp263-284.html
   My bibliography  Save this article

On the choice of denominator functions and convergence of NSFD schemes for a class of nonlinear SBVPs

Author

Listed:
  • Kayenat, Sheerin
  • Verma, Amit Kumar

Abstract

We propose two novel non-standard finite difference (NSFD) schemes for a class of non-linear singular boundary value problems (SBVPs). One of the basic idea of NSFD schemes is that the step size Δt is replaced by a non-linear function, e.g., sinΔt, tanΔt etc. In the present work, we propose to include one more parameter in the non-linear denominator functions (DFs), e.g., in place of tanΔt, we propose to use ktan(Δt/k), where k∈[c,∞) with c∈R+ which further accelerates the accuracy and reduces the CPU time. We have applied this idea to solve generalized class of non-linear doubly singular BVPs. We observe that there exist some optimal values of k that give much better results. We determine the value of k by experimenting with various DFs on the proposed NSFD schemes. Further it will be interesting to see if we can find out optimal value of k analytically and whether this optimal value is unique. Convergence of the proposed NSFD schemes has also been proved. The results have been verified by several test examples. The results have been compared with other existing methods and matlab bvp4c solver, which shows the applicability and effectiveness of the proposed NSFD schemes.

Suggested Citation

  • Kayenat, Sheerin & Verma, Amit Kumar, 2022. "On the choice of denominator functions and convergence of NSFD schemes for a class of nonlinear SBVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 263-284.
    • Handle: RePEc:eee:matcom:v:200:y:2022:i:c:p:263-284
    DOI: 10.1016/j.matcom.2022.04.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422001616
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.04.019?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. Amit K. Verma & Biswajit Pandit & Lajja Verma & Ravi P. Agarwal, 2020. "A Review on a Class of Second Order Nonlinear Singular BVPs," Mathematics, MDPI, vol. 8(7), pages 1-50, June.
    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. Rawani, Mukesh Kumar & Verma, Amit Kumar & Verma, Lajja, 2024. "Numerical treatment of Burgers' equation based on weakly L-stable generalized time integration formula with the NSFD scheme," Applied Mathematics and Computation, Elsevier, vol. 467(C).

    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.

      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:200:y:2022:i:c:p:263-284. 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.