A Reduced-Order Finite Difference Scheme Based on POD for Fractional Stochastic Advection-Diffusion Equation

Abstract

his article introduces a new scheme for the fractional stochastic advection-diffusion equation (FSA-DE) in time where the fractional term is expressed in Caputo sence of order (0 <a<1). First, an L1 approximation is employed to estimate the Caputo derivative. Then, the spatial derivative is approximated 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, the POD based reduced-order IFD scheme is obtained. The proposed scheme can be regarded as the modification of the exiting work (Mirzaee et al. in J Sci Technol Trans Sci 45:607-617, 2001). The numerical results are provided to confirm the feasibility and efficiency of the proposed method.