Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear multistep methods for integrating reversible differential
  equations   This paper studies multistep methods for the integration of reversible
dynamical systems, with particular emphasis on the planar Kepler problem. It
has previously been shown by Cano & Sanz-Serna that reversible linear
multisteps for first-order differential equations are generally unstable. Here,
we report on a subset of these methods -- the zero-growth methods -- that evade
these instabilities. We provide an algorithm for identifying these rare
methods. We find and study all zero-growth, reversible multisteps with six or
fewer steps. This select group includes two well-known second-order multisteps
(the trapezoidal and explicit midpoint methods), as well as three new
fourth-order multisteps -- one of which is explicit. Variable timesteps can be
readily implemented without spoiling the reversibility. Tests on Keplerian
orbits show that these new reversible multisteps work well on orbits with low
or moderate eccentricity, although at least 100 steps/radian are required for
stability.

7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci