IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v349y2019icp304-313.html
   My bibliography  Save this article

Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments

Author

Listed:
  • Li, Xiuying
  • Li, Haixia
  • Wu, Boying

Abstract

In this paper, we introduce a piecewise reproducing kernel method for impulsive delay differential equations with piecewise constant arguments. The method is an improved reproducing kernel method. Compared with the classical reproducing kernel method, the solutions obtained using the present method can give good approximations for a larger time interval. Some numerical examples are used to show the effectiveness and simplicity of the method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:304-313
    DOI: 10.1016/j.amc.2018.12.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318311159
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.12.054?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. 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.
    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. Zhang, G.L. & Song, Minghui & Liu, M.Z., 2015. "Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 12-21.
    4. Ghasemi, M. & Fardi, M. & Khoshsiar Ghaziani, R., 2015. "Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 815-831.
    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. 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.
    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. 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).
    4. Hartung, Ferenc, 2022. "On numerical approximation of a delay differential equation with impulsive self-support condition," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    5. 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).
    6. 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.
    7. 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.
    8. Allahviranloo, Tofigh & Sahihi, Hussein, 2021. "Reproducing kernel method to solve fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 400(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.
    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. Zhang, Gui-Lai, 2022. "Convergence, consistency and zero stability of impulsive one-step numerical methods," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    3. 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).
    4. Zhang, Gui-Lai, 2017. "High order Runge–Kutta methods for impulsive delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 12-23.
    5. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    6. Rengamannar, Kaviya & Balakrishnan, Ganesh Priya & Palanisamy, Muthukumar & Niezabitowski, Michal, 2020. "Exponential stability of non-linear stochastic delay differential system with generalized delay-dependent impulsive points," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    7. Wu, Jie & He, Xinyi & Li, Xiaodi, 2022. "Finite-time stabilization of time-varying nonlinear systems based on a novel differential inequality approach," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    8. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    9. 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.
    10. Chen, Zhong & Gou, QianQian, 2019. "Piecewise Picard iteration method for solving nonlinear fractional differential equation with proportional delays," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 465-478.
    11. Hartung, Ferenc, 2022. "On numerical approximation of a delay differential equation with impulsive self-support condition," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    12. Gui-Lai Zhang & Chao Liu, 2024. "Two Schemes of Impulsive Runge–Kutta Methods for Linear Differential Equations with Delayed Impulses," Mathematics, MDPI, vol. 12(13), pages 1-17, July.
    13. 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.
    14. Du, Mingjing & Qiao, Xiaohua & Wang, Biao & Wang, Yulan & Gao, Bo, 2019. "A novel method for numerical simulation of sand motion model in beach formation based on fractional Taylor–Jumarie series expansion and piecewise interpolation technique," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 15-21.
    15. Kaviya, R. & Priyanka, M. & Muthukumar, P., 2022. "Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 160(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:349:y:2019:i:c:p:304-313. 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.