Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the long-time integration of stochastic gradient systems   This article addresses the weak convergence of numerical methods for Brownian
dynamics. Typical analyses of numerical methods for stochastic differential
equations focus on properties such as the weak order which estimates the
asymptotic (stepsize $h \to 0$) convergence behavior of the error of finite
time averages. Recently it has been demonstrated, by study of Fokker-Planck
operators, that a non-Markovian numerical method [Leimkuhler and Matthews,
2013; Leimkuhler et al., 2013] generates approximations in the long time limit
with higher accuracy order (2nd order) than would be expected from its weak
convergence analysis (finite-time averages are 1st order accurate). In this
article we describe the transition from the transient to the steady-state
regime of this numerical method by estimating the time-dependency of the
coefficients in an asymptotic expansion for the weak error, demonstrating that
the convergence to 2nd order is exponentially rapid in time. Moreover, we
provide numerical tests of the theory, including comparisons of the
efficiencies of the Euler-Maruyama method, the popular 2nd order Heun method,
and the non-Markovian method.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol