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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
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    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, 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.
    3. 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.
    4. 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.
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