Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On compact 4th order finite-difference schemes for the wave equation   We consider compact finite-difference schemes of the 4th approximation order
for an initial-boundary value problem (IBVP) for the $n$-dimensional
non-homogeneous wave equation, $n\geq 1$. Their construction is accomplished by
both the classical Numerov approach and alternative technique based on
averaging of the equation, together with further necessary improvements of the
arising scheme for $n\geq 2$. The alternative technique is applicable to other
types of PDEs including parabolic and time-dependent Schr\"{o}dinger ones. The
schemes are implicit and three-point in each spatial direction and time and
include a scheme with a splitting operator for $n\geq 2$. For $n=1$ and the
mesh on characteristics, the 4th order scheme becomes explicit and close to an
exact four-point scheme. We present a conditional stability theorem covering
the cases of stability in strong and weak energy norms with respect to both
initial functions and free term in the equation. Its corollary ensures the 4th
order error bound in the case of smooth solutions to the IBVP. The main schemes
are generalized for non-uniform rectangular meshes. We also give results of
numerical experiments showing the sensitive dependence of the error orders in
three norms on the weak smoothness order of the initial functions and free term
and essential advantages over the 2nd approximation order schemes in the
non-smooth case as well.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
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The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph