Numerical Methods for Approximating Stochastic Semilinear Time-Fractional Rayleigh-Stokes Equations (Journal of Computational Mathematics, 2024)
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 fractionaltime-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 finiteelement method, and the error estimate is analyzed. A convolution quadrature methodgenerated by the backward Euler method is employed for the time discretization resultingin a fully discrete scheme. The error estimate for the fully discrete solution is consideredbased on the regularity of the solution, and a strong convergence rate is established. Thepaper concludes with numerical tests to validate the theoretical findings.