Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and dynamical properties of Rosenau-Hyman compactons using
  Pade approximants   We present a systematic approach for calculating higher-order derivatives of
smooth functions on a uniform grid using Pad\'e approximants. We illustrate our
findings by deriving higher-order approximations using traditional second-order
finite-differences formulas as our starting point. We employ these schemes to
study the stability and dynamical properties of K(2,2) Rosenau-Hyman (RH)
compactons including the collision of two compactons and resultant shock
formation. Our approach uses a differencing scheme involving only nearest and
next-to-nearest neighbors on a uniform spatial grid. The partial differential
equation for the compactons involves first, second and third partial
derivatives in the spatial coordinate and we concentrate on four different
fourth-order methods which differ in the possibility of increasing the degree
of accuracy (or not) of one of the spatial derivatives to sixth order. A method
designed to reduce roundoff errors was found to be the most accurate
approximation in stability studies of single solitary waves, even though all
derivates are accurate only to fourth order. Simulating compacton scattering
requires the addition of fourth derivatives related to artificial viscosity.
For those problems the different choices lead to different amounts of
"spurious" radiation and we compare the virtues of the different choices.

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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom