High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

Chen, S., Jiang, X., Liu, F., & Turner, I. (2015) High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation. Journal of Computational and Applied Mathematics, 278, pp. 119-129.

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Abstract

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

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5 citations in Web of Science®

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ID Code: 82651
Item Type: Journal Article
Refereed: Yes
DOI: 10.1016/j.cam.2014.09.028
ISSN: 0377-0427
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Dynamical Systems in Applications (010204)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Divisions: Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS)
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2015 Elsevier
Copyright Statement: This is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, [VOL 278, (2015)] DOI: 10.1016/j.cam.2014.09.028
Deposited On: 22 Mar 2015 23:16
Last Modified: 14 Dec 2015 04:00

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