Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Properties of four numerical schemes applied to a scalar nonlinear
  scalar wave equation with a GR-type nonlinearity   We study stability, dispersion and dissipation properties of four numerical
schemes (Iterative Crank-Nicolson, 3'rd and 4'th order Runge-Kutta and
Courant-Fredrichs-Levy Non-linear). By use of a Von Neumann analysis we study
the schemes applied to a scalar linear wave equation as well as a scalar
non-linear wave equation with a type of non-linearity present in GR-equations.
Numerical testing is done to verify analytic results. We find that the method
of lines (MOL) schemes are the most dispersive and dissipative schemes. The
Courant-Fredrichs-Levy Non-linear (CFLN) scheme is most accurate and least
dispersive and dissipative, but the absence of dissipation at Nyquist
frequency, if fact, puts it at a disadvantage in numerical simulation. Overall,
the 4'th order Runge-Kutta scheme, which has the least amount of dissipation
among the MOL schemes, seems to be the most suitable compromise between the
overall accuracy and damping at short wavelengths.

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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol