Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric spaces and Lie triple systems in numerical analysis of
  differential equations   A remarkable number of different numerical algorithms can be understood and
analyzed using the concepts of symmetric spaces and Lie triple systems, which
are well known in differential geometry from the study of spaces of constant
curvature and their tangents. This theory can be used to unify a range of
different topics, such as polar-type matrix decompositions, splitting methods
for computation of the matrix exponential, composition of selfadjoint numerical
integrators and dynamical systems with symmetries and reversing symmetries. The
thread of this paper is the following: involutive automorphisms on groups
induce a factorization at a group level, and a splitting at the algebra level.
In this paper we will give an introduction to the mathematical theory behind
these constructions, and review recent results. Furthermore, we present a new
Yoshida-like technique, for self-adjoint numerical schemes, that allows to
increase the order of preservation of symmetries by two units. Since all the
time-steps are positive, the technique is particularly suited to stiff
problems, where a negative time-step can cause instabilities.

18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin