Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A numerical study of the homogeneous elliptic equation with fractional
  order boundary conditions   We consider the homogeneous equation ${\mathcal A} u=0$, where ${\mathcal A}$
is a symmetric and coercive elliptic operator in $H^1(\Omega)$ with $\Omega$
bounded domain in ${{\mathbb R}}^d$. The boundary conditions involve fractional
power $\alpha$, $ 0 < \alpha <1$, of the Steklov spectral operator arising in
Dirichlet to Neumann map. For such problems we discuss two different numerical
methods: (1) a computational algorithm based on an approximation of the
integral representation of the fractional power of the operator and (2)
numerical technique involving an auxiliary Cauchy problem for an
ultra-parabolic equation and its subsequent approximation by a time stepping
technique. For both methods we present numerical experiment for a model
two-dimensional problem that demonstrate the accuracy, efficiency, and
stability of the algorithms.

28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an