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

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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.

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Author information

Authors and Affiliations

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

    Fawang Liu

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

    Mark M. Meerschaert

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

    Robert J. McGough

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

    Pinghui Zhuang & Qingxia Liu

Authors
  1. Fawang Liu
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  2. Mark M. Meerschaert
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  3. Robert J. McGough
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  4. Pinghui Zhuang
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  5. Qingxia Liu
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Corresponding author

Correspondence to Fawang Liu.

Additional information

Editorial Note: The first author Fawang Liu received the ”Mittag-Leffler Award: FDA Achievement Award” at the 2012 Symposium on Fractional Differentiation and Its Applications (FDA’2012), Hohai University, Nanjing.

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Liu, F., Meerschaert, M.M., McGough, R.J. et al. Numerical methods for solving the multi-term time-fractional wave-diffusion equation. fcaa 16, 9–25 (2013). https://doi.org/10.2478/s13540-013-0002-2

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  • DOI: https://doi.org/10.2478/s13540-013-0002-2

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