Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A semi-discrete numerical method for convolution-type unidirectional
  wave equations   Numerical approximation of a general class of nonlinear unidirectional wave
equations with a convolution-type nonlocality in space is considered. A
semi-discrete numerical method based on both a uniform space discretization and
the discrete convolution operator is introduced to solve the Cauchy problem.
The method is proved to be uniformly convergent as the mesh size goes to zero.
The order of convergence for the discretization error is linear or quadratic
depending on the smoothness of the convolution kernel. The discrete problem
defined on the whole spatial domain is then truncated to a finite domain.
Restricting the problem to a finite domain introduces a localization error and
it is proved that this localization error stays below a given threshold if the
finite domain is large enough. For two particular kernel functions, the
numerical examples concerning solitary wave solutions illustrate the expected
accuracy of the method. Our class of nonlocal wave equations includes the
Benjamin-Bona-Mahony equation as a special case and the present work is
inspired by the previous work of Bona, Pritchard and Scott on numerical
solution of the Benjamin-Bona-Mahony equation.

24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess