Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Approach for Deriving Optimal Finite Differences   A unified approach to derive optimal finite differences is presented which
combines three critical elements for numerical performance especially for
multi-scale physical problems, namely, order of accuracy, spectral resolution
and stability. The resulting mathematical framework reduces to a minimization
problem subjected to equality and inequality constraints. We show that the
framework can provide analytical results for optimal schemes and their
numerical performance including, for example, the type of errors that appear
for spectrally optimal schemes. By coupling the problem in this unified
framework, one can effectively decouple the requirements for order of accuracy
and spectral resolution, for example. Alternatively, we show how the framework
exposes the tradeoffs between e.g. accuracy and stability and how this can be
used to construct explicit schemes that remain stable with very large time
steps. We also show how spectrally optimal schemes only bias odd-order
derivatives to remain stable, at the expense of accuracy, while leaving
even-order derivatives with symmetric coefficients. Schemes constructed within
this framework are tested for diverse model problems with an emphasis on
reproducing the physics accurately.

11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th