A fast algorithm for solving the variable-order (VO) time-fractional diffusion equations. At first, we develop a fast method applying the sum-of-exponentials technique to approximate the VO Caputo fractional derivative. Compared with the general direct method, the proposed method can reduce the storage requirement from  to  and computational cost from  to , respectively, with  being the number of the time levels. In addition, this fast method is then used to construct a finite difference scheme to discretize the VO time-fractional diffusion equations. The computational complexity of the proposed scheme is of  with storage requirement, where  denotes the number of spatial grids. Theoretically, the stability and the convergence of the proposed scheme are further investigated. The effectiveness of the proposal algorithm is verified by numerical examples.

会议ID：895 442 769