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

      Wang, Junmei; orcid: ; email: 39041@llhc.edu.cn; Hoult, James; orcid: ; email: 1405193@chester.ac.uk; Yan, Yubin; orcid: 0000-0002-5686-5017; email: y.yan@chester.ac.uk (MDPI, 2021-08-12)
      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.