Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomized exponential integrators for modulated nonlinear Schr\"odinger
  equations   We consider the nonlinear Schr\"odinger equation with dispersion modulated by
a (formal) derivative of a time-dependent function with fractional Sobolev
regularity of class $W^{\alpha,2}$ for some $\alpha\in (0,1)$. Due to the loss
of smoothness in the problem classical numerical methods face severe order
reduction. In this work, we develop and analyze a new randomized exponential
integrator based on a stratified Monte Carlo approximation. The new
discretization technique averages the high oscillations in the solution
allowing for improved convergence rates of order $\alpha+1/2$. In addition, the
new approach allows us to treat a far more general class of modulations than
the available literature. Numerical results underline our theoretical findings
and show the favorable error behavior of our new scheme compared to classical
methods.

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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int