An asymptotic preserving scheme for Lévy-Fokker-Planck equation with fractional diffusion limit

03/16/2021
by   Wuzhe Xu, et al.
0

In this paper, we develop a numerical method for the Lévy-Fokker-Planck equation with the fractional diffusive scaling. There are two main challenges. One comes from a two-fold nonlocality, that is, the need to apply the fractional Laplacian operator to a power law decay distribution. The other arises from long-time/small mean-free-path scaling, which introduces stiffness to the equation. To resolve the first difficulty, we use a change of variable to convert the unbounded domain into a bounded one and then apply the Chebyshev polynomial based pseudo-spectral method. To treat the multiple scales, we propose an asymptotic preserving scheme based on a novel micro-macro decomposition that uses the structure of the test function in proving the fractional diffusion limit analytically. Finally, the efficiency and accuracy of our scheme are illustrated by a suite of numerical examples.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/25/2022

Uniform error estimate of an asymptotic preserving scheme for the Lévy-Fokker-Planck equation

We establish a uniform-in-scaling error estimate for the asymptotic pres...
research
10/22/2020

An efficient spectral-Galerkin method for fractional reaction-diffusion equations in unbounded domains

In this work, we apply a fast and accurate numerical method for solving ...
research
09/15/2023

A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains

We propose a new fractional Laplacian for bounded domains, expressed as ...
research
02/25/2023

A high-order discrete energy decay and maximum-principle preserving scheme for time fractional Allen-Cahn equation

The shifted fractional trapezoidal rule (SFTR) with a special shift is a...
research
06/17/2022

An efficient spectral method for the fractional Schrödinger equation on the real line

The fractional Schrödinger equation (FSE) on the real line arises in a b...
research
11/25/2019

Structure-preserving algorithms for multi-dimensional fractional Klein-Gordon-Schrödinger equation

This paper aims to construct structure-preserving numerical schemes for ...
research
09/04/2019

Vibration Analysis of Geometrically Nonlinear and Fractional Viscoelastic Cantilever Beams

We investigate the nonlinear vibration of a fractional viscoelastic cant...

Please sign up or login with your details

Forgot password? Click here to reset