Reduced order finite difference scheme based on POD for fractional stochastic advection-diffusion equation

This paper introduce a numerical solution of time fractional stochastic advection-diffusion equa- tion (FSA-DE) wherein time fractional derivative is described in Caputo sence of order α (0 < α < 1). First, a L1 approximation is employed to estimate the Caputo derivative. Then, the spatial derivative is discretized by a second-order finite difference scheme. Moreover, we combine the implicit finite difference (IFD) scheme with the proper orthogonal decomposition (POD) method to reduce the used cpu time. In other words, we obtain POD based reduced-order IFD scheme. As a result, the new scheme can be viewed as the modification of the exiting job (Mirzaee et al., 2020 [23]). The numerical results provide to verify the feasibility and efficiency of the new method.