Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Solution Method for Numerical Solving of the Wave Propagation
  Problem   A new method for numerical solving of boundary problem for ordinary
differential equations with slowly varying coefficients which is aimed at
better representation of solutions in the regions of their rapid oscillations
or exponential increasing (decreasing) is proposed. It is based on
approximation of the solution to find in the form of superposition of certain
polynomial- exponential basic functions. The method is studied for the
Helmholtz equation in comparison with the standard finite difference method.
The numerical tests have shown the convergence of the method proposed. In
comparison with the finite difference method the same accuracy is obtained on
substantially rarer mesh. This advantage becomes more pronounced, if the
solution varies very rapidly.

28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga