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Fractional Calculus and Applied Analysis

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Volume 16, Issue 1

Issues

Numerical methods for solving the multi-term time-fractional wave-diffusion equation

Fawang Liu
  • School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia
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/ Mark Meerschaert / Robert McGough / Pinghui Zhuang / Qingxia Liu
Published Online: 2012-12-27 | DOI: https://doi.org/10.2478/s13540-013-0002-2

Abstract

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

MSC: 26A33 (main); 65M22; 35L05; 35J05

Keywords: multi-term time fractional wave-diffusion equations; Caputo derivative; a power law wave equation; finite difference method; fractional predictor-corrector method

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About the article

Published Online: 2012-12-27

Published in Print: 2013-03-01


Citation Information: Fractional Calculus and Applied Analysis, Volume 16, Issue 1, Pages 9–25, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-013-0002-2.

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© 2013 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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