Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving highly-oscillatory NLS with SAM: numerical efficiency and
  geometric properties   In this paper, we present the Stroboscopic Averaging Method (SAM), recently
introduced in [7,8,10,12], which aims at numerically solving highly-oscillatory
differential equations. More specifically, we first apply SAM to the
Schr\"odinger equation on the 1-dimensional torus and on the real line with
harmonic potential, with the aim of assessing its efficiency: as compared to
the well-established standard splitting schemes, the stiffer the problem is,
the larger the speed-up grows (up to a factor 100 in our tests). The geometric
properties of SAM are also explored: on very long time intervals, symmetric
implementations of the method show a very good preservation of the mass
invariant and of the energy. In a second series of experiments on 2-dimensional
equations, we demonstrate the ability of SAM to capture qualitatively the
long-time evolution of the solution (without spurring high oscillations).

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The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
18
The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn