English

Convergence of a stochastic particle approximation for fractional scalar conservation laws

Probability 2010-07-26 v1 Analysis of PDEs

Abstract

We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation uses a system of particles driven by L\'evy alpha-stable processes and interacting with their drift through their empirical cumulative distribution function. We show convergence to the solution for the associated Euler scheme.

Keywords

Cite

@article{arxiv.1006.4047,
  title  = {Convergence of a stochastic particle approximation for fractional scalar conservation laws},
  author = {Benjamin Jourdain and Raphaël Roux},
  journal= {arXiv preprint arXiv:1006.4047},
  year   = {2010}
}