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Spatial Discretization for Stochastic Semi-Linear Subdiffusion Equations Driven by Fractionally Integrated Multiplicative Space-Time White Noise
Yan, Yubin Hoult, James Wang, Junmei
Yan, Yubin
Hoult, James
Wang, Junmei
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2021-08-12
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Abstract
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/math9161917
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MDPI
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Mathematics
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10.3390/math9161917
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Article
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2227-7390