Numerical methods for solving the multi-term time-fractional wave-diffusion equation-Reference-Cited by-同舟云学术

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

Published:2012-12-27 Issue:1 Volume:16 Page:9-25
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Liu Fawang¹,Meerschaert Mark²,McGough Robert³,Zhuang Pinghui⁴,Liu Qingxia⁴

Affiliation:

1. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia

2. Department of Statistics and Probability, Michigan State University, East Lansing, Michigan, 48824, USA

3. Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan, 48824, USA

4. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P.R. China

Abstract

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.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

Link

http://link.springer.com/content/pdf/10.2478/s13540-013-0002-2.pdf

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