Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900737 | Applied Mathematics and Computation | 2018 | 18 Pages |
Abstract
In this paper, a second-order accurate implicit scheme based on the L2-1Ï formula for temporal variable and the fractional centered difference formula for spatial discretization is established to solve a class of time-space fractional diffusion equations with time drift term and non-linear delayed source function. The stability of this scheme is proved rigorously by the discrete energy method under several auxiliary assumptions, then we theoretically and numerically show that the proposed scheme converges in the L2-norm with the order O((Ît)2+h2) with time step Ît and mesh size h. Moreover, it finds that the discreted linear systems are symmetric Toeplitz systems. In order to solve these systems efficiently, the conjugate gradient method with suitable circulant preconditioners is designed. In each iterative step, the storage requirements and the computational complexity of the resulting equations are O(N) and O(NlogN) respectively, where N is the number of grid nodes. Numerical experiments are carried out to demonstrate the effectiveness of our proposed circulant preconditioners.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Yong-Liang Zhao, Pei-Yong Zhu, Wei-Hua Luo,