TY - JOUR
T1 - Numerical Analysis for Stochastic Time-Space Fractional Diffusion Equation Driven by Fractional Gaussian Noise
AU - Nie , Daxin
AU - Deng , Weihua
JO - Journal of Computational Mathematics
VL - 6
SP - 1502
EP - 1525
PY - 2024
DA - 2024/11
SN - 42
DO - http://doi.org/10.4208/jcm.2305-m2023-0014
UR - https://global-sci.org/intro/article_detail/jcm/23505.html
KW - Fractional Laplacian, Stochastic fractional diffusion equation, Fractional Gaussian noise, Finite element, Convolution quadrature, Error analysis.
AB - <p style="text-align: justify;">In this paper, we consider the strong convergence of the time-space fractional diffusion equation driven by fractional Gaussian noise with Hurst index $H ∈ (1/2, 1).$ A sharp
regularity estimate of the mild solution and the numerical scheme constructed by finite element method for integral fractional Laplacian and backward Euler convolution quadrature
for Riemann-Liouville time fractional derivative are proposed. With the help of inverse
Laplace transform and fractional Ritz projection, we obtain the accurate error estimates in
time and space. Finally, our theoretical results are accompanied by numerical experiments.</p>