Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Holistic finite differences ensure fidelity to Burger's equation   I analyse a generalised Burger's equation to develop an accurate finite
difference approximation to its dynamics. The analysis is based upon centre
manifold theory so we are assured that the finite difference model accurately
models the dynamics and may be constructed systematically. The trick to the
application of centre manifold theory is to divide the physical domain into
small elements by introducing insulating internal boundaries which are later
removed. Burger's equation is used as an example to show how the concepts work
in practise. The resulting finite difference models are shown to be
significantly more accurate than conventional discretisations, particularly for
highly nonlinear dynamics. This centre manifold approach treats the dynamical
equations as a whole, not just as the sum of separate terms---it is holistic.
The techniques developed here may be used to accurately model the nonlinear
evolution of quite general spatio-temporal dynamical systems.

10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph