Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modified energy for split-step methods applied to the linear
  Schr\"odinger equation   We consider the linear Schr\"odinger equation and its discretization by
split-step methods where the part corresponding to the Laplace operator is
approximated by the midpoint rule. We show that the numerical solution
coincides with the exact solution of a modified partial differential equation
at each time step. This shows the existence of a modified energy preserved by
the numerical scheme. This energy is close to the exact energy if the numerical
solution is smooth. As a consequence, we give uniform regularity estimates for
the numerical solution over arbitrary long time

8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg