Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear gradient structures and discrete gradient methods for
  conservative/dissipative differential-algebraic equations   In this paper, we consider the use of discrete gradients for
differential-algebraic equations (DAEs) with a conservation/dissipation law. As
one of the most popular numerical methods for conservative/dissipative ordinary
differential equations, the framework of discrete gradient methods has been
intensively developed over recent decades. Although discrete gradients have
been applied to several specific conservative/dissipative DAEs, no unified
framework for DAEs has yet been constructed. In this paper, we move toward the
establishment of such a framework, and introduce concepts including an
appropriate linear gradient structure for DAEs. Then, we reveal that the simple
use of discrete gradients does not imply the discrete conservation/dissipation
laws. Fortunately, however, we can successfully construct a new discrete
gradient method for the case of index-1 DAEs. We believe this first attempt
provides an indispensable basis for constructing a unified framework of
discrete gradient methods for DAEs.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an