Numerical Analysis for Stochastic Time-Space Fractional Diffusion Equation Driven by Fractional Gaussian Noise
Year: 2024
Author: Daxin Nie, Weihua Deng
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1502–1525
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2305-m2023-0014
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1502–1525
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Fractional Laplacian Stochastic fractional diffusion equation Fractional Gaussian noise Finite element Convolution quadrature Error analysis.
Author Details
Daxin Nie Email
Weihua Deng Email