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 - <p style="text-align: justify;">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.</p>