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Mathematical Problems in Engineering
Volume 2014, Article ID 194249, 5 pages
Research Article

An Efficient Iteration Method for Toeplitz-Plus-Band Triangular Systems Generated from Fractional Ordinary Differential Equation

1College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
2Science and Technology on Space Physics Laboratory, Beijing 100076, China
3School of Computer Science, National University of Defense Technology, Changsha 410073, China

Received 2 January 2014; Accepted 27 May 2014; Published 12 June 2014

Academic Editor: Riccardo Caponetto

Copyright © 2014 Chunye Gong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is time consuming to numerically solve fractional differential equations. The fractional ordinary differential equations may produce Toeplitz-plus-band triangular systems. An efficient iteration method for Toeplitz-plus-band triangular systems is presented with computational complexity and memory complexity in this paper, compared with the regular solution with computational complexity and memory complexity. is the discrete grid points. Some methods such as matrix splitting, FFT, compress memory storage and adjustable matrix bandwidth are used in the presented solution. The experimental results show that the presented method compares well with the exact solution and is 4.25 times faster than the regular solution.