Online First
Numerical Methods for Approximating Stochastic Semilinear Time-Fractional Rayleigh-Stokes Equations
Mariam Al-Maskari

J. Comp. Math. DOI: 10.4208/jcm.2311-m2023-0047

Publication Date : 2024-03-19

  • 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.

  • Copyright

COPYRIGHT: © Global Science Press