We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

An asymptotic preserving method for Levy Fokker Planck equation with fractional diffusion limit

Formal Metadata

Title
An asymptotic preserving method for Levy Fokker Planck equation with fractional diffusion limit
Title of Series
Number of Parts
19
Author
Contributors
License
CC Attribution - NonCommercial - NoDerivatives 2.0 Generic:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
We develop a numerical method for the Levy-Fokker-Planckequation with the fractional diffusive scaling. There are two main challenges. One comes from a two-fold nonlocality, that is, the need to apply the frac-tional Laplacian operator to a power law decay distribution. The other comes from long-time/small mean-free-path scaling, which calls for a uniform stablesolver. To resolve the first difficulty, we use a change of variable to convert theunbounded domain into a bounded one and then apply Chebyshev polyno-mial based pseudo-spectral method. To resolve the second issue, we propose an asymptotic preserving scheme based on a novel micro-macro decomposition that uses the structure of the test function in proving the fractionaldiffusion limit analytically.