Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-product operator splitting as a general method of solving
  autonomous and non-autonomous equations   Prior to the recent development of symplectic integrators, the time-stepping
operator $\e^{h(A+B)}$ was routinely decomposed into a sum of products of
$\e^{h A}$ and $\e^{hB}$ in the study of hyperbolic partial differential
equations. In the context of solving Hamiltonian dynamics, we show that such a
decomposition give rises to both {\it even} and {\it odd} order Runge-Kutta and
Nystr\"om integrators. By use of Suzuki's forward-time derivative operator to
enforce the time-ordered exponential, we show that the same decomposition can
be used to solve non-autonomous equations. In particular, odd order algorithms
are derived on the basis of a highly non-trivial {\it time-asymmetric} kernel.
Such an operator approach provides a general and unified basis for
understanding structure non-preserving algorithms and is especially useful in
deriving very high-order algorithms via {\it analytical} extrapolations. In
this work, algorithms up to the 100th order are tested by integrating the
ground state wave function of the hydrogen atom. For such a singular Coulomb
problem, the multi-product expansion showed uniform convergence and is free of
poles usually associated with structure-preserving methods. Other examples are
also discussed.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat