IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1917-d612805.html
   My bibliography  Save this article

Spatial Discretization for Stochastic Semi-Linear Subdiffusion Equations Driven by Fractionally Integrated Multiplicative Space-Time White Noise

Author

Listed:
  • Junmei Wang

    (Department of Mathematics, LuLiang University, Lishi 033000, China
    These authors contributed equally to this work.)

  • James Hoult

    (Department of Mathematical and Physical Sciences, University of Chester, Chester CH1 4BJ, UK
    These authors contributed equally to this work.)

  • Yubin Yan

    (Department of Mathematical and Physical Sciences, University of Chester, Chester CH1 4BJ, UK
    These authors contributed equally to this work.)

Abstract

Spatial discretization of the stochastic semi-linear subdiffusion equations driven by fractionally integrated multiplicative space-time white noise is considered. The nonlinear terms f and σ satisfy the global Lipschitz conditions and the linear growth conditions. The space derivative and the fractionally integrated multiplicative space-time white noise are discretized by using the finite difference methods. Based on the approximations of the Green functions expressed by the Mittag–Leffler functions, the optimal spatial convergence rates of the proposed numerical method are proved uniformly in space under some suitable smoothness assumptions of the initial value.

Suggested Citation

  • Junmei Wang & James Hoult & Yubin Yan, 2021. "Spatial Discretization for Stochastic Semi-Linear Subdiffusion Equations Driven by Fractionally Integrated Multiplicative Space-Time White Noise," Mathematics, MDPI, vol. 9(16), pages 1-38, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1917-:d:612805
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1917/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1917/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Becker, Sebastian & Jentzen, Arnulf, 2019. "Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg–Landau equations," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 28-69.
    2. Chen, Le & Hu, Yaozhong & Nualart, David, 2019. "Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5073-5112.
    3. Chen, Zhen-Qing & Kim, Kyeong-Hun & Kim, Panki, 2015. "Fractional time stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1470-1499.
    4. Lord, Gabriel J. & Tambue, Antoine, 2018. "A modified semi–implicit Euler–Maruyama scheme for finite element discretization of SPDEs with additive noise," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 105-122.
    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. Wang, Xiaojie, 2020. "An efficient explicit full-discrete scheme for strong approximation of stochastic Allen–Cahn equation," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6271-6299.
    2. Tambue, Antoine & Mukam, Jean Daniel, 2019. "Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear SPDEs driven by multiplicative or additive noise," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 23-40.
    3. Asogwa, Sunday A. & Nane, Erkan, 2017. "Intermittency fronts for space-time fractional stochastic partial differential equations in (d+1) dimensions," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1354-1374.
    4. Sweilam, N.H. & El-Sakout, D.M. & Muttardi, M.M., 2020. "Numerical study for time fractional stochastic semi linear advection diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Cui, Jianbo & Hong, Jialin & Sun, Liying, 2021. "Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 55-93.
    6. Chen, Le & Hu, Yaozhong & Nualart, David, 2019. "Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5073-5112.
    7. Zou, Guang-an & Lv, Guangying & Wu, Jiang-Lun, 2018. "On the regularity of weak solutions to space–time fractional stochastic heat equations," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 84-89.
    8. Kumar, Vivek, 2022. "Stochastic fractional heat equation perturbed by general Gaussian and non-Gaussian noise," Statistics & Probability Letters, Elsevier, vol. 184(C).
    9. Liu, Xinfei & Yang, Xiaoyuan, 2023. "Numerical approximation of the stochastic equation driven by the fractional noise," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    10. Tuan, Nguyen Huy & Caraballo, Tomás & Thach, Tran Ngoc, 2023. "New results for stochastic fractional pseudo-parabolic equations with delays driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 24-67.
    11. Giordano, Luca M. & Jolis, Maria & Quer-Sardanyons, Lluís, 2020. "SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7396-7430.

    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:9:y:2021:i:16:p:1917-:d:612805. 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.