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Volume 42, Issue 6
Numerical Analysis for Stochastic Time-Space Fractional Diffusion Equation Driven by Fractional Gaussian Noise

Daxin Nie & Weihua Deng

DOI: 10.4208/jcm.2305-m2023-0014

J. Comp. Math., 42 (2024), pp. 1502-1525.

Published online: 2024-11

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  • 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.

  • Keywords

Fractional Laplacian, Stochastic fractional diffusion equation, Fractional Gaussian noise, Finite element, Convolution quadrature, Error analysis.

  • AMS Subject Headings

65M12, 65M60, 35R11, 35R60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-1502, author = {Nie , Daxin and Deng , Weihua}, title = {Numerical Analysis for Stochastic Time-Space Fractional Diffusion Equation Driven by Fractional Gaussian Noise}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2305-m2023-0014}, url = {http://global-sci.org/intro/article_detail/jcm/23505.html} }
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 -

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.

Nie , Daxin and Deng , Weihua. (2024). Numerical Analysis for Stochastic Time-Space Fractional Diffusion Equation Driven by Fractional Gaussian Noise. Journal of Computational Mathematics. 42 (6). 1502-1525. doi:10.4208/jcm.2305-m2023-0014
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