Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evaluating the Pixel Array Method as Applied to Partial Differential
  Equations   The Pixel Array (PA) Method, originally introduced by Spivak et. al., is a
fast method for solving nonlinear or linear systems. One of its distinguishing
features is that it presents all solutions within a bounding box, represented
by a plot whose axes are the values of "exposed variables." Here we develop a
set-theoretic variant of the PA method, named the Pixel Array Solution-Set
(PASS) method, that gives PA access to "hidden variables" whose values are not
displayed on plot axes. We evaluate the effectiveness of PASS at numerically
finding steady states for several partial differential equations. We discretize
several one-dimensional solved reaction-diffusion equations, such as the Fisher
equation and the Benjamin-Bona-Mohany equation, using finite differences. Then,
we run PASS on each equation, and determine whether it successfully finds all
boundary conditions for which a numerical steady state might exist. Then we
verify whether the steady states found by PASS are correct. Finally, we discuss
the benefits and weaknesses of PASS.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat