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High-order explicit-implicit numerical methods for nonlinear anomalous diffusion equations

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Abstract

In this paper, the high-order finite difference/element methods for the nonlinear anomalous diffusion equations of subdiffusion and superdiffusion are developed, where the high-order finite difference methods are used to approximate the time-fractional derivatives and the finite element methods are used in the spatial domain. The stability and error estimates are proved for both cases of superdiffusion and subdiffusion. Numerical examples are provided to confirm the theoretical analysis.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, 200444, Shanghai, China

    F. Zeng & C. Li

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

    F. Liu

Authors
  1. F. Zeng
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  2. C. Li
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  3. F. Liu
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Corresponding author

Correspondence to C. Li.

Additional information

The present work was supported by the National Natural Science Foundation of China (No. 11372170), the grant of The First-class Discipline of Universities in Shanghai, the Key Program of Shanghai Municipal Education Commission (No. 12ZZ084), and the China Scholarship Council (No. 201206890032).

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Zeng, F., Li, C. & Liu, F. High-order explicit-implicit numerical methods for nonlinear anomalous diffusion equations. Eur. Phys. J. Spec. Top. 222, 1885–1900 (2013). https://doi.org/10.1140/epjst/e2013-01971-3

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  • DOI: https://doi.org/10.1140/epjst/e2013-01971-3

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