Finite Difference/Spectral Approximations For The Two-Dimensional Time Caputo-Fabrizio Fractional Diffusion Equation

The main contribution of this work is to construct and analyze stable and high order schemes to efficiently solve the two-dimensional time Caputo-Fabrizio fractional diffusion equation.Based on a third-order finite difference method in time and spectral methods in space,the proposed scheme is unconditionally stable and has the global truncation error O(?³+N^-m),where?,N and m are the time step size,polynomial degree and regularity in the space variable of the exact solution,respectively.It should be noted that the global truncation error O(?²+N^-m)is well established in[Li,Lv and Xu,Numer.Methods Partial Differ.Equ.?2019?].Finally,some numerical experiments are carried out to verify the theoretical analysis.To the best of our knowledge,this is the first proof for the stability of the third-order scheme for the Caputo-Fabrizio fractional operator.