IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v423y2022ics0096300322001035.html
   My bibliography  Save this article

Convergence, consistency and zero stability of impulsive one-step numerical methods

Author

Listed:
  • Zhang, Gui-Lai

Abstract

Impulsive one-step numerical methods are defined in the present paper, especially, a common and widely used numerical form generalised from Runge-Kutta methods defined as impulsive Runge-Kutta methods. And it is proved that a consistent and zero-stable method thus convergent. Moreover, it is also proved that an impulsive one-step numerical method is convergent of order p if the corresponding method is pth order. Another equivalent form of impulsive one-step numerical methods are also introduced. In addition, numerical experiments are provided to illustrate the advantage of impulsive Runge-Kutta methods.

Suggested Citation

  • Zhang, Gui-Lai, 2022. "Convergence, consistency and zero stability of impulsive one-step numerical methods," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    • Handle: RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300322001035
    DOI: 10.1016/j.amc.2022.127017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322001035
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127017?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. Zhang, Gui-Lai & Song, Ming-Hui, 2019. "Impulsive continuous Runge–Kutta methods for impulsive delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 160-173.
    2. Liu, X. & Zeng, Y.M., 2018. "Linear multistep methods for impulsive delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 555-563.
    3. Liming Wang & Baoqing Yang & Xiaohua Ding & Kai-Ning Wu, 2015. "Boundedness of Stochastic Delay Differential Systems with Impulsive Control and Impulsive Disturbance," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, March.
    4. Xiaotai Wu & Litan Yan & Wenbing Zhang & Liang Chen, 2012. "Exponential Stability of Impulsive Stochastic Delay Differential Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-15, January.
    5. 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.
    6. Kaining Wu & Xiaohua Ding, 2012. "Stability and Stabilization of Impulsive Stochastic Delay Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-16, May.
    7. Kaining Wu & Xiaohua Ding & Liming Wang, 2010. "Stability and Stabilization of Impulsive Stochastic Delay Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-15, March.
    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. 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.
    2. Zuo, Hujian & Zhao, Weifeng & Lin, Ping, 2022. "Boundary treatment of linear multistep methods for hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. 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.
    4. Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.
    5. Hartung, Ferenc, 2022. "On numerical approximation of a delay differential equation with impulsive self-support condition," Applied Mathematics and Computation, Elsevier, vol. 418(C).

    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:423:y:2022:i:c:s0096300322001035. 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.