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

Junmei Wang, James Hoult and Yubin Yan
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Junmei Wang: Department of Mathematics, LuLiang University, Lishi 033000, China
James Hoult: Department of Mathematical and Physical Sciences, University of Chester, Chester CH1 4BJ, UK
Yubin Yan: Department of Mathematical and Physical Sciences, University of Chester, Chester CH1 4BJ, UK

Mathematics, 2021, vol. 9, issue 16, 1-38

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 ? 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.

Keywords: semi-linear; space-time white noise; Caputo fractional derivative; fractionally integrated additive noise; error estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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