Strong Approximation of Stochastic Subdiffusion Driven by Integrated Multiplicative Space-Time White Noise

Abstract

This paper investigates the strong convergence of a numerical method for stochastic subdiffusion, which involves a Caputo derivative in time of order [inline-graphic not available: see fulltext], and is driven by fractionally integrated multiplicative space-time white noise. A spatio-temporal full discretization method, based on the fractional exponential integrator scheme and the finite element method, is constructed and analyzed. The error estimation is quite complex due to the following inherent difficulties: (i) the solution operator corresponding to the mild solution does not satisfy the semigroup property because of the memory effects induced by the fractional derivative, (ii) the space-time white noise is coarser than the general trace class noise, and the regularity of the solution is very low. The well-posedness of the underlying equation is established via the equivalent norm, and a sharp strong convergence rate of the fully discrete solution is derived using Mainardi’s Wright function. Finally, numerical experiments are presented to validate the theoretical results.

Keywords

Stochastic subdiffusion / Multiplicative space-time white noise / Fractional exponential integrator scheme / Finite element method / Strong convergence / 60H15 / 65C30 / 60H35 / 74S60

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Funding

The Research Fund of Jianghan University(2024JCYJ04)

RIGHTS & PERMISSIONS

Shanghai University

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