Denys Dutykh
All publications
2019

Numerical simulation of Feller's diffusion equation

MMathematics
D. Dutykh
Mathematics 7(11): 1067 (2019)
Open Access
HAL VersionPublisher VersionDOI

Abstract

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

Keywords

Feller's diffusion equationnumerical simulationprobability density functionLagrangian fluid mechanicsparabolic equationsstability conditionopen source softwarewave turbulence theoryFeller equationnumerical schemeLagrangian scheme

Bibliographic record

Journal: Mathematics
Volume: 7
Issue: 11
Pages: 1067
arXiv: 1909.10944

BibTeX Citation

@article{Dutykh2019numericalsimulation,
  author = {Dutykh, D.},
  title = {Numerical simulation of Feller's diffusion equation},
  journal = {Mathematics},
  year = {2019},
  volume = {7},
  number = {11},
  pages = {1067},
  doi = {10.3390/math7111067},
  abstract = {This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.},
  keywords = {Feller's diffusion equation, numerical simulation, probability density function, Lagrangian fluid mechanics, parabolic equations, stability condition, open source software, wave turbulence theory, Feller equation, numerical scheme, Lagrangian scheme}
}