Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Implicit Methods for Equation-Free Analysis: Convergence Results and
  Analysis of Emergent Waves in Microscopic Traffic Models   We introduce a general formulation for an implicit equation-free method in
the setting of slow-fast systems. First, we give a rigorous convergence result
for equation-free analysis showing that the implicitly defined coarse-level
time stepper converges to the true dynamics on the slow manifold within an
error that is exponentially small with respect to the small parameter measuring
time scale separation. Second, we apply this result to the idealized traffic
modeling problem of phantom jams generated by cars with uniform behavior on a
circular road. The traffic jams are waves that travel slowly against the
direction of traffic. Equation-free analysis enables us to investigate the
behavior of the microscopic traffic model on a macroscopic level. The standard
deviation of cars' headways is chosen as the macroscopic measure of the
underlying dynamics such that traveling wave solutions correspond to equilibria
on the macroscopic level in the equation-free setup. The collapse of the
traffic jam to the free flow then corresponds to a saddle-node bifurcation of
this macroscopic equilibrium. We continue this bifurcation in two parameters
using equation-free analysis.

8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics