Spatial Discretization for Stochastic Semi-Linear Subdiffusion Equations Driven by Fractionally Integrated Multiplicative Space-Time White Noise
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University of Chester; LuLiang UniversityPublication Date
2021-08-12
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Spatial 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.Citation
Wang, 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/math9161917Publisher
MDPIJournal
MathematicsAdditional Links
https://www.mdpi.com/2227-7390/9/16/1917Type
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2227-7390ae974a485f413a2113503eed53cd6c53
10.3390/math9161917
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