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arXiv · 1810.01822

Numerical Approximation of Stochastic Time-Fractional Diffusion

Bangti Jin·Yubin Yan·Zhi Zhou
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Abstract

We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order $\alpha\in(0,1)$, and fractionally integrated Gaussian noise (with a Riemann-Liouville fractional integral of order $\gamma \in[0,1]$ in the front). The numerical scheme approximates the model in space by the Galerkin method with continuous piecewise linear finite elements and in time by the classical Gr\"unwald-Letnikov method, and the noise by the $L^2$-projection. Sharp strong and weak convergence rates are established, using suitable nonsmooth data error estimates for the deterministic counterpart. Numerical results are presented to support the theoretical findings.

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Bangti Jin, Yubin Yan, Zhi Zhou. 2018-10-03. Numerical Approximation of Stochastic Time-Fractional Diffusion. https://arxiv.org/abs/1810.01822

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