Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-similarly corrected Pade approximants for nonlinear equations   We consider the problem of finding approximate analytical solutions for
nonlinear equations typical of physics applications. The emphasis is on the
modification of the method of Pad\'e approximants that are known to provide the
best approximation for the class of rational functions, but do not provide
sufficient accuracy or cannot be applied at all for those nonlinear problems,
whose solutions exhibit behaviour characterized by irrational functions. In
order to improve the accuracy, we suggest a method of self-similarly corrected
Pad\'e approximants, taking into account irrational functional behaviour. The
idea of the method is in representing the sought solution as a product of two
factors, one of which is given by a self-similar root approximant, responsible
for irrational functional behaviour, and the other being a Pad\'e approximant
corresponding to a rational function. The efficiency of the method is
illustrated by constructing very accurate solutions for nonlinear differential
equations. A thorough investigation is given proving that the suggested method
is more accurate than the method of standard Pad\'e approximants.

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The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph