Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The space-fractional diffusion-advection equation: Analytical solutions
  and critical assessment of numerical solutions   The present work provides a critical assessment of numerical solutions of the
space-fractional diffusion-advection equation, which is of high significance
for applications in various natural sciences. In view of the fact that, in
contrast to the case of normal (Gaussian) diffusion, no standard methods and
corresponding numerical codes for anomalous diffusion problems have been
established yet, it is of importance to critically assess the accuracy and
performance of existing approaches. Three numerical methods, namely a
finite-difference method, the so-called matrix transfer technique, and a
Monte-Carlo method based on the solution of stochastic differential equations,
are analyzed and compared by applying them to three selected test problems for
which analytical or semi-analytical solutions were known or are newly derived.
The accuracy and performance differences are critically discussed with the
result that the use of stochastic differential equations appears to be
advantageous.

37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph