Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Basins of attraction and critical curves for Newton-type methods in a
  phase equilibrium problem   Many engineering problems are described by systems of nonlinear equations,
which may exhibit multiple solutions, in a challenging situation for
root-finding algorithms. The existence of several solutions may give rise to
complex basins of attraction for the solutions in the algorithms, with severe
influence in their convergence behavior. In this work, we explore the
relationship of the basins of attractions with the critical curves (the locus
of the singular points of the Jacobian of the system of equations) in a phase
equilibrium problem in the plane with two solutions, namely the calculation of
a double azeotrope in a binary mixture. The results indicate that the conjoint
use of the basins of attraction and critical curves can be a useful tool to
select the most suitable algorithm for a specific problem.

19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th