An Accelerated Convergence Scheme for Solving Stochastic Fractional Diffusion Equation

An accelerated convergence scheme for temporal approximation of stochastic partial differential equation is presented. First, the regularity of the mild solution is provided. Combining the It & ocirc; formula and the remainder term of the exponential Euler scheme, this paper proposes a high accuracy time discretization method. Based on regularity results, a strong convergence rate for the discretization error O(tau(3/2-epsilon)) is proved for arbitrarily small epsilon > 0. Here tau is the uniform time step size. Finally, the theoretical results are verified by several numerical experiments.