Yan, YubinHoult, JamesWang, Junmei2021-10-012021-10-012021-08-12Wang, J., Hoult, J., Yan, Y. (2021). Spatial discretization for stochastic semi-linear subdiffusion equations driven by fractionally integrated multiplicative space-time white noise. Mathematics, 9(16), 1917. https://doi.org/10.3390/math9161917No print ISSN10.3390/math9161917http://hdl.handle.net/10034/626003Spatial discretization of the stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise is considered. The spatial discretization scheme discussed in Gy\"ongy \cite{gyo_space} and Anton et al. \cite{antcohque} for stochastic quasi-linear parabolic partial differential equations driven by multiplicative space-time noise is extended to the stochastic subdiffusion. The nonlinear terms $f$ and $\sigma$ satisfy the global Lipschitz conditions and the linear growth conditions. The space derivative and the integrated multiplicative space-time white noise are discretized by using finite difference methods. Based on the approximations of the Green functions which are expressed with the Mittag-Leffler functions, the optimal spatial convergence rates of the proposed numerical method are proved uniformly in space under the suitable smoothness assumptions of the initial values.https://creativecommons.org/licenses/by/4.0/semi-linearspace-time white noiseCaputo fractional derivativefractionally integrated additive noiseerror estimatesArticle2227-7390Mathematics