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Volume 43, Issue 3
Numerical Methods for Approximating Stochastic Semilinear Time-Fractional Rayleigh-Stokes Equations

Mariam Al-Maskari

DOI: 10.4208/jcm.2311-m2023-0047

J. Comp. Math., 43 (2025), pp. 569-587.

Published online: 2024-11

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  • Abstract

This paper investigates a semilinear stochastic fractional Rayleigh-Stokes equation featuring a Riemann-Liouville fractional derivative of order $α ∈ (0, 1)$ in time and a fractional time-integral noise. The study begins with an examination of the solution’s existence, uniqueness, and regularity. The spatial discretization is then carried out using a finite element method, and the error estimate is analyzed. A convolution quadrature method generated by the backward Euler method is employed for the time discretization resulting in a fully discrete scheme. The error estimate for the fully discrete solution is considered based on the regularity of the solution, and a strong convergence rate is established. The paper concludes with numerical tests to validate the theoretical findings.

  • Keywords

Riemann-Liouville fractional derivative, Stochastic Rayleigh-Stokes equation, Finite element method, Convolution quadrature, Error estimates.

  • AMS Subject Headings

65M60, 65M12, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-569, author = {Al-Maskari , Mariam}, title = {Numerical Methods for Approximating Stochastic Semilinear Time-Fractional Rayleigh-Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {43}, number = {3}, pages = {569--587}, abstract = {

This paper investigates a semilinear stochastic fractional Rayleigh-Stokes equation featuring a Riemann-Liouville fractional derivative of order $α ∈ (0, 1)$ in time and a fractional time-integral noise. The study begins with an examination of the solution’s existence, uniqueness, and regularity. The spatial discretization is then carried out using a finite element method, and the error estimate is analyzed. A convolution quadrature method generated by the backward Euler method is employed for the time discretization resulting in a fully discrete scheme. The error estimate for the fully discrete solution is considered based on the regularity of the solution, and a strong convergence rate is established. The paper concludes with numerical tests to validate the theoretical findings.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2311-m2023-0047}, url = {http://global-sci.org/intro/article_detail/jcm/23550.html} }
TY - JOUR T1 - Numerical Methods for Approximating Stochastic Semilinear Time-Fractional Rayleigh-Stokes Equations AU - Al-Maskari , Mariam JO - Journal of Computational Mathematics VL - 3 SP - 569 EP - 587 PY - 2024 DA - 2024/11 SN - 43 DO - http://doi.org/10.4208/jcm.2311-m2023-0047 UR - https://global-sci.org/intro/article_detail/jcm/23550.html KW - Riemann-Liouville fractional derivative, Stochastic Rayleigh-Stokes equation, Finite element method, Convolution quadrature, Error estimates. AB -

This paper investigates a semilinear stochastic fractional Rayleigh-Stokes equation featuring a Riemann-Liouville fractional derivative of order $α ∈ (0, 1)$ in time and a fractional time-integral noise. The study begins with an examination of the solution’s existence, uniqueness, and regularity. The spatial discretization is then carried out using a finite element method, and the error estimate is analyzed. A convolution quadrature method generated by the backward Euler method is employed for the time discretization resulting in a fully discrete scheme. The error estimate for the fully discrete solution is considered based on the regularity of the solution, and a strong convergence rate is established. The paper concludes with numerical tests to validate the theoretical findings.

Al-Maskari , Mariam. (2024). Numerical Methods for Approximating Stochastic Semilinear Time-Fractional Rayleigh-Stokes Equations. Journal of Computational Mathematics. 43 (3). 569-587. doi:10.4208/jcm.2311-m2023-0047
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