L1 Scheme for Semilinear Stochastic Subdiffusion with Integrated Fractional Gaussian Noise

This paper considers a numerical method for solving the stochastic semilinear subdiffusion equation which is driven by integrated fractional Gaussian noise and the Hurst parameter H is an element of(1/2,1). The finite element method is employed for spatial discretization, while the L1 scheme and Lubich's first-order convolution quadrature formula are used to approximate the Caputo time-fractional derivative of order alpha is an element of(0,1) and the Riemann-Liouville time-fractional integral of order gamma is an element of(0,1), respectively. Using the semigroup approach, we establish the temporal and spatial regularity of the mild solution to the problem. The fully discrete solution is expressed as a convolution of a piecewise constant function with the inverse Laplace transform of a resolvent-related function. Based on the Laplace transform method and resolvent estimates, we prove that the proposed numerical scheme has the optimal convergence order O(tau(min{H+alpha+gamma-1-epsilon,alpha)}),epsilon>0. Numerical experiments are presented to validate these theoretical convergence orders and demonstrate the effectiveness of this method.