Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical integration of ODEs while preserving all polynomial first
  integrals   We present a novel method for solving ordinary differential equations (ODEs)
while preserving all polynomial first integrals. The method is essentially a
symplectic Runge-Kutta method applied to a reformulated version of the ODE
under study and is illustrated through a number of examples including
Hamiltonian ODEs, a Nambu system and the Toda Lattice. When applied to certain
Hamiltonian ODEs, the proposed method yields the averaged vector field method
as a special case.

0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg