A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative
Numerical Analysis
2011-09-13 v1 Computational Physics
Abstract
A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method is derived. The stability of this scheme is established by von Neumann analysis. Some numerical results are shown, which demonstrate the efficiency and convergence of the method. Additionally, some physical properties of this fractional diffusion system are simulated, which further confirm the effectiveness of our method.
Keywords
Cite
@article{arxiv.1109.2345,
title = {A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative},
author = {Ercília Sousa and Can Li},
journal= {arXiv preprint arXiv:1109.2345},
year = {2011}
}