An efficient iteration method for Toeplitz-plus-band triangular systems generated from fractional ordinary differential equation
type: Item
instance of: scholarly article
title: An efficient iteration method for Toeplitz-plus-band triangular systems generated from fractional ordinary differential equation
zbMATH Open document ID: 1407.65039
DOI: 10.1155/2014/194249
author: Chunye Gong
author: Changwan Min
author: Jie Liu
author: Wei-min Bao
author: Guo-Jian Tang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: 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 \(O \left(M \text{l} \text{o} \text{g} \left(M\right)\right)\) computational complexity and \(O \left(M\right)\) memory complexity in this paper, compared with the regular solution with \(O \left(M^2\right)\) computational complexity and \(O \left(M^2\right)\) memory complexity. \(M\) 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.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 7015885
Wikidata QID: Q59063685
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/194249
OpenAlex ID: W2138540163
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description: scientific article; zbMATH DE number 7015885