Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of Painlev\'e II on real intervals: novel approximating
  sequences   Novel sequences of approximants to solutions of Painlev\'e II on finite
intervals of the real line, with Neumann boundary conditions, are constructed.
Numerical experiments strongly suggest convergence of these sequences in a
surprisingly wide range of cases, even ones where ordinary perturbation series
fail to converge. These sequences are here labeled extraordinary because of
their unusual properties. Each element of such a sequence is defined on its own
interval. As the sequence (apparently) converges to a solution of the
corresponding boundary value problem for Painlev\'e II, these intervals
themselves (apparently) converge to the defining interval for that problem, and
an associated sequence of constants (apparently) converges to the constant term
in the Painlev\'e II equation itself. Each extraordinary sequence is
constructed in a nonlinear fashion from a perturbation series approximation to
the solution of a supplementary boundary value problem, involving a
generalization of Painlev\'e II that arises in studies of electrodiffusion.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat