IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v418y2022ics0096300321009012.html
   My bibliography  Save this article

On numerical approximation of a delay differential equation with impulsive self-support condition

Author

Listed:
  • Hartung, Ferenc

Abstract

In this paper we consider a scalar linear delay equation with constant delay associated with an impulsive self-support condition. We define a numerical approximation scheme using a sequence of approximate delay equations with piecewise constant arguments, and we show its theoretical convergence. We present numerical examples to illustrate the applicability of the method, and we also observe existence of periodic solutions of the impulsive delay equation using numerical studies.

Suggested Citation

  • Hartung, Ferenc, 2022. "On numerical approximation of a delay differential equation with impulsive self-support condition," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009012
    DOI: 10.1016/j.amc.2021.126818
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321009012
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126818?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. M. Shah & Joseph Wiener, 1983. "Advanced differential equations with piecewise constant argument deviations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-33, January.
    2. X. Liu & M. H. Song & M. Z. Liu, 2012. "Linear Multistep Methods for Impulsive Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-14, May.
    3. Li, Xiuying & Li, Haixia & Wu, Boying, 2019. "Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 304-313.
    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. Liu, X. & Zeng, Y.M., 2019. "Analytic and numerical stability of delay differential equations with variable impulses," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 293-304.
    2. Hao Ma & Jian Pan & Lei Lv & Guanghui Xu & Feng Ding & Ahmed Alsaedi & Tasawar Hayat, 2019. "Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    3. Li, X.Y. & Wu, B.Y., 2020. "A new kernel functions based approach for solving 1-D interface problems," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    4. Allahviranloo, Tofigh & Sahihi, Hussein, 2021. "Reproducing kernel method to solve fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    5. Li, Xiuying & Li, Haixia & Wu, Boying, 2019. "Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 304-313.
    6. Geng, F.Z. & Wu, X.Y., 2021. "Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    7. Xiao Zhang & Feng Ding & Ling Xu & Ahmed Alsaedi & Tasawar Hayat, 2019. "A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise," Mathematics, MDPI, vol. 7(4), pages 1-17, April.
    8. James Guyker, 2015. "Periodic Solutions of Certain Differential Equations with Piecewise Constant Argument," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-17, July.
    9. Assanova, Anar T. & Uteshova, Roza, 2022. "Solution of a nonlocal problem for hyperbolic equations with piecewise constant argument of generalized type," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    10. Zhang, Gui-Lai, 2022. "Convergence, consistency and zero stability of impulsive one-step numerical methods," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    11. Feng Ding & Jian Pan & Ahmed Alsaedi & Tasawar Hayat, 2019. "Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    12. Lijuan Wan & Ximei Liu & Feng Ding & Chunping Chen, 2019. "Decomposition Least-Squares-Based Iterative Identification Algorithms for Multivariable Equation-Error Autoregressive Moving Average Systems," Mathematics, MDPI, vol. 7(7), pages 1-20, July.

    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:418:y:2022:i:c:s0096300321009012. 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.