Fractional Diffusion Equations (FDEs)

In this page you can see and download some Mathematica notebooks that show how to solve FDEs by means of the methods discussed in:

S. B. Yuste and L. Acedo, On an explicit finite difference method for fractional diffusion equations, arXiv:cs/0311011v1 [cs.NA] (2003); S. B. Yuste and L. Acedo, An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations, SIAM Journal of Numerical Analysis, 52, 1862-74 (2005).
- The notebook corresponding to this method is FractionalExplicitMethod.nb The pdf version of this notebook is FractionalExplicitMethod.pdf
S. B. Yuste, Weighted average finite difference methods for fractional diffusion equations, Proceedings of FDA’04, pages 335-340 (2004) (see also arXiv:cs/0408053v1 [cs.NA] (2004) ) and S. B. Yuste, Weighted average finite difference methods for fractional diffusion equations,Journal of Computational Physics 216 (2006) 264-274 [DOI: 10.1016/j.jcp.2005.12.006 . One gets a fractional version of the Crank-Nicolson method if one chooses the weight factor λ=1/2. You can find a detailed notebook on this fractional Crank-Nicolson in the Wolfram notebook archive Numerical method à la Crank-Nicolson for fractional diffusion equationsHere you can find:
- A Mathematica notebook that uses this method: FractionalWeightedAveragedMethod.nb
- A pdf version, FractionalWeightedAveragedMethod .pdf, of the notebook FractionalWeightedAveragedMethod.nb
- A Wolfram Demonstration Project in which this method is used: “Numerical Solution of Some Fractional Diffusion Equations ” from The Wolfram Demonstrations Project
S. B. Yuste and J. Quintana-Murillo. Fast, Accurate and Robust Adaptive Finite Difference Methods for Fractional Diffusion Equations.Numerical Algorithms, 71 (1) pp 207-228 (2016) [ pdf ]
- The notebook corresponding to this method is Adaptative L1 TE and Predictive.nb The pdf version of this notebook is Adaptative L1 TE and Predictive.pdf