Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability properties of a projector-splitting scheme for dynamical low
  rank approximation of random parabolic equations   We consider the Dynamical Low Rank (DLR) approximation of random parabolic
equations and propose a class of fully discrete numerical schemes. Similarly to
the continuous DLR approximation, our schemes are shown to satisfy a discrete
variational formulation. By exploiting this property, we establish stability of
our schemes: we show that our explicit and semi-implicit versions are
conditionally stable under a parabolic type CFL condition which does not depend
on the smallest singular value of the DLR solution; whereas our implicit scheme
is unconditionally stable. Moreover, we show that, in certain cases, the
semi-implicit scheme can be unconditionally stable if the randomness in the
system is sufficiently small. Furthermore, we show that these schemes can be
interpreted as projector-splitting integrators and are strongly related to the
scheme proposed by Lubich et al. [BIT Num. Math., 54:171-188, 2014; SIAM J. on
Num. Anal., 53:917-941, 2015], to which our stability analysis applies as well.
The analysis is supported by numerical results showing the sharpness of the
obtained stability conditions.

12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess