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The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1885–1900 | Cite as

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

  • F. Zeng
  • C. Li
  • F. Liu
Regular Article

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.

Keywords

European Physical Journal Special Topic Convergence Order Time Direction Liouville Derivative Time Fractional Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina
  2. 2.School of Mathematical SciencesQueensland University of TechnologyBrisbaneAustralia

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