부산대학교 도서관

Generally, solving linear systems from finite difference alternating direction implicit scheme of two-dimensional time-space fractional differential equations with Gaussian elimination requires O NM 1 M 2 M 1 2 + M 2 2 + N M 1 M 2 complexity and O N M 1 2 M 2 2 storage, where N is the number of temporal unknown and M1, M2 are the numbers of spatial unknown in x, y directions respectively. By exploring the structure of the coefficient matrix in fully coupled form, it possesses block lower-triangular Toeplitz structure and its blocks are block-dense Toeplitz matrices with dense-Toeplitz blocks. Based on this special structure and cooperating with time-marching or divide-and-conquer technique, two fast solvers with storage O NM 1 M 2 are developed. The complexity for the fast solver via time-marching is O NM 1 M 2 N + log M 1 M 2 and the one via divide-and-conquer technique is O NM 1 M 2 log 2 N + log M 1 M 2 . It is worth to remark that the proposed solvers are not lossy. Some discussions on achieving convergence rate for smooth and non-smooth solutions are given. Numerical results show the high efficiency of the proposed fast solvers. [ABSTRACT FROM AUTHOR]