Stability and convergence of an implicit numerical method for the non-linear fractional reaction–subdiffusion process

Australian Research Council [DP0559807, DP0986766]; National Natural Science Foundation of China [10271098]; National Science Foundation of China [10726061]; Natural Science Foundation of Fujian Province [Z0511009]

[1]  S. Wearne,et al.  Anomalous subdiffusion with multispecies linear reaction dynamics. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  S L Wearne,et al.  Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  I. Sokolov,et al.  Mesoscopic description of reactions for anomalous diffusion: a case study , 2006, cond-mat/0608117.

[4]  I M Sokolov,et al.  Reaction-subdiffusion equations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Fawang Liu,et al.  Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method , 2007, J. Comput. Phys..

[6]  Fawang Liu,et al.  New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation , 2008, SIAM J. Numer. Anal..

[7]  Fawang Liu,et al.  Numerical solution of the space fractional Fokker-Planck equation , 2004 .

[8]  I. Podlubny.  Fractional differential equations , 1998 .

[9]  Fawang Liu,et al.  Fractional high order methods for the nonlinear fractional ordinary differential equation , 2007 .

[10]  Fawang Liu,et al.  Implicit difference approximation for the time fractional diffusion equation , 2006 .

[11]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[12]  S. Wearne,et al.  Fractional Reaction-Diffusion , 2000 .

[13]  B. Henry,et al.  The accuracy and stability of an implicit solution method for the fractional diffusion equation , 2005 .

[14]  J. P. Roop.  Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in R 2 , 2006 .

[15]  M. Meerschaert,et al.  Finite difference approximations for two-sided space-fractional partial differential equations , 2006 .

[16]  S B Yuste,et al.  Subdiffusion-limited A+A reactions. , 2001, Physical review letters.

[17]  Mark M. Meerschaert,et al.  A second-order accurate numerical approximation for the fractional diffusion equation , 2006, J. Comput. Phys..

[18]  Santos B. Yuste,et al.  An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations , 2004, SIAM J. Numer. Anal..

[19]  M. Meerschaert,et al.  Finite difference approximations for fractional advection-dispersion flow equations , 2004 .

[20]  Santos B. Yuste,et al.  Subdiffusion-limited A+A reactions. , 2001 .

[21]  Katja Lindenberg,et al.  Reaction front in an A+B-->C reaction-subdiffusion process. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[23]  I. Turner,et al.  Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation , 2005 .

[24]  Kazuhiko Seki,et al.  Fractional reaction-diffusion equation , 2003 .