Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of Invariant Measure for Damped Stochastic Nonlinear
  Schr\"{o}dinger Equation via an Ergodic Numerical Scheme   In order to inherit numerically the ergodicity of the damped stochastic
nonlinear Schr\"odinger equation with additive noise, we propose a fully
discrete scheme, whose spatial direction is based on spectral Galerkin method
and temporal direction is based on a modification of the implicit Euler scheme.
We not only prove the unique ergodicity of the numerical solutions of both
spatial semi-discretization and full discretization, but also present error
estimations on invariant measures, which gives order $2$ in spatial direction
and order ${\frac12}$ in temporal direction.

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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg