IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i18p3366-d916540.html
   My bibliography  Save this article

The Improved Stability Analysis of Numerical Method for Stochastic Delay Differential Equations

Author

Listed:
  • Yu Zhang

    (School of Economics, Harbin University of Commerce, Harbin 150028, China)

  • Enying Zhang

    (School of Economics, Harbin University of Commerce, Harbin 150028, China)

  • Longsuo Li

    (School of Management, Harbin Institute of Technology, Harbin 150001, China)

Abstract

In this paper, the improved split-step θ method, named the split-step composite θ method, is proposed to study the mean-square stability for stochastic differential equations with a fixed time delay. Under the global Lipschitz and linear growth conditions, it is proved that the split-step composite θ method with θ ≥ 0.5 shows mean-square stability. An approach to improving numerical stability is illustrated by choices of parameters of this method. Some numerical examples are presented to show the accordance between the theoretical and numerical results.

Suggested Citation

  • Yu Zhang & Enying Zhang & Longsuo Li, 2022. "The Improved Stability Analysis of Numerical Method for Stochastic Delay Differential Equations," Mathematics, MDPI, vol. 10(18), pages 1-7, September.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3366-:d:916540
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/18/3366/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/18/3366/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liu, Linna & Mo, Haoyi & Deng, Feiqi, 2019. "Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 320-328.
    2. Zhao, Guihua & Song, Minghui & Yang, Zhanwen, 2015. "Mean-square stability of analytic solution and Euler–Maruyama method for impulsive stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 527-538.
    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, Zhao-Yan & Shang, Shengnan & Lam, James, 2019. "On stability of neutral-type linear stochastic time-delay systems with three different delays," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 147-166.
    2. Liu, Linna & Zhu, Quanxin, 2015. "Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 698-712.
    3. Amr Abosenna & Ghada AlNemer & Boping Tian, 2024. "Convergence and Almost Sure Polynomial Stability of Partially Truncated Split-Step Theta Method for Stochastic Pantograph Models with Lévy Jumps," Mathematics, MDPI, vol. 12(13), pages 1-16, June.
    4. Song, Minghui & Geng, Yidan & Liu, Mingzhu, 2021. "Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods," Applied Mathematics and Computation, Elsevier, vol. 400(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:gam:jmathe:v:10:y:2022:i:18:p:3366-:d:916540. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.