Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An asymptotic preserving scheme for L\'{e}vy-Fokker-Planck equation with
  fractional diffusion limit   In this paper, we develop a numerical method for the L\'evy-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.

8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org