Eur. Phys. J. Special Topics 222, 1885-1900 (2013)
https://doi.org/10.1140/epjst/e2013-01971-3

Regular Article

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

¹ Department of Mathematics, Shanghai University, Shanghai 200444, China
² School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia

^a e-mail: lcp{at}shu{dot}edu{dot}cn

Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013

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.