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. LiEmail author
  • F. Liu
Regular Article


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.


European Physical Journal Special Topic Convergence Order Time Direction Liouville Derivative Time Fractional Derivative 
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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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