Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial Spectral collocation Method for Space Fractional
  Advection-Diffusion Equation   This paper discusses the spectral collocation method for numerically solving
nonlocal problems: one dimensional space fractional advection-diffusion
equation; and two dimensional linear/nonlinear space fractional
advection-diffusion equation. The differentiation matrixes of the left and
right Riemann-Liouville and Caputo fractional derivatives are derived for any
collocation points within any given interval. The stabilities of the one
dimensional semi-discrete and full-discrete schemes are theoretically
established. Several numerical examples with different boundary conditions are
computed to testify the efficiency of the numerical schemes and confirm the
exponential convergence; the physical simulations for L\'evy-Feller
advection-diffusion equation are performed; and the eigenvalue distributions of
the iterative matrix for a variety of systems are displayed to illustrate the
stabilities of the numerical schemes in more general cases.

30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph