Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Spectral Method for the Eigenvalue Problem for Elliptic Equations   Let $\Omega$ be an open, simply connected, and bounded region in
$\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth.
Consider solving the eigenvalue problem $Lu=\lambda u$ for an elliptic partial
differential operator $L$ over $\Omega$ with zero values for either Dirichlet
or Neumann boundary conditions. We propose, analyze, and illustrate a 'spectral
method' for solving numerically such an eigenvalue problem. This is an
extension of the methods presented earlier in [5],[6].

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an