Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some methods for solving equations with an operator function and
  applications for problems with a fractional power of an operator   Several applied problems are characterized by the need to numerically solve
equations with an operator function (matrix function). In particular, in the
last decade, mathematical models with a fractional power of an elliptic
operator and numerical methods for their study have been actively discussed.
Computational algorithms for such non-standard problems are based on
approximations by the operator function. The most widespread are the approaches
using various options for rational approximation. Also, we note the methods
that relate to approximation by exponential sums. In this paper, the
possibility of using approximation by exponential products is noted. The
solution of an equation with an operator function is based on the transition to
standard stationary or evolutionary problems. General approaches are
illustrated by a problem with a fractional power of the operator. The first
class of methods is based on the integral representation of the operator
function under rational approximation, approximation by exponential sums, and
approximation by exponential products. The second class of methods is
associated with solving an auxiliary Cauchy problem for some evolutionary
equation.

36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph