Corpus ID: 236469494

On a structure-preserving numerical method for fractional Fokker-Planck equations

@article{Ayi2021OnAS,
  title={On a structure-preserving numerical method for fractional Fokker-Planck equations},
  author={N. Ayi and M. Herda and H{\'e}l{\`e}ne Hivert and Isabelle Tristani},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.13416}
}
In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic Lévy-Fokker-Planck equation. The discretizations are designed to preserve the main features of the continuous model such as conservation of mass, heavy-tailed equilibrium and (hypo)coercivity properties. We perform a thorough analysis of the numerical scheme and show exponential stability. Along the way, we introduce new tools of discrete functional analysis, such as discrete nonlocal Poincaré and… Expand

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