A finite difference method with non-uniform timesteps for fractional diffusion equations

@article{Yuste2012AFD,
  title={A finite difference method with non-uniform timesteps for fractional diffusion equations},
  author={Santos B. Yuste and Joaqu{\'i}n Quintana-Murillo},
  journal={Computer Physics Communications},
  year={2012},
  volume={183},
  pages={2594-2600}
}
An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the behavior of the solution in order to keep the numerical errors small without the penalty of a huge computational cost. Themethod is unconditionally stable and convergent. In fact, it is shown that consistency and stability implies convergence for a rather… CONTINUE READING

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