The accuracy and stability of an implicit solution method for the fractional diffusion equation

  • Authors:

  • T. A. M. Langlands;B. I. Henry

  • Affiliations:

  • Department of Applied Mathematics, School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia;Department of Applied Mathematics, School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

We have investigated the accuracy and stability of an implicit numerical scheme for solving the fractional diffusion equation. This model equation governs the evolution for the probability density function that describes anomalously diffusing particles. Anomalous diffusion is ubiquitous in physical and biological systems where trapping and binding of particles can occur. The implicit numerical scheme that we have investigated is based on finite difference approximations and is straightforward to implement. The accuracy of the scheme is O(@Dx^2) in the spatial grid size and O(@Dt^1^+^@c) in the fractional time step, where 0=