Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functionally-fitted explicit pseudo two-step Runge-Kutta-Nystr\"om
  methods   A general class of functionally-fitted explicit pseudo two-step
Runge-Kutta-Nystr\"{o}m (FEPTRKN) methods for solving second-order initial
value problems has been studied. These methods can be considered generalized
explicit pseudo two-step Runge-Kutta-Nystr\"{o}m (EPTRKN) methods. We proved
that an $s$-stage FEPTRKN method has step order $p = s$ and stage order $r = s$
for any set of distinct collocation parameters $(c_i)_{i=1}^s$.
Supperconvergence for the accuracy orders of these methods can be obtained if
the collocation parameters $(c_i)_{i=1}^s$ satisfy some orthogonality
conditions. We proved that an $s$-stage FEPTRKN method can attain accuracy
order $p = s + 3$. Numerical experiments have shown that the new FEPTRKN
methods work better than do EPTRKN methods on problems whose solutions can be
well approximated by the functions in bases on which these FEPTRKN methods are
developed.

16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th