Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Class of $A$ Stable Summation by Parts Time Integration Schemes
  with Strong Initial Conditions   Since integration by parts is an important tool when deriving energy or
entropy estimates for differential equations, one may conjecture that some form
of summation by parts (SBP) property is involved in provably stable numerical
methods. This article contributes to this topic by proposing a novel class of
$A$ stable SBP time integration methods which can also be reformulated as
implicit Runge-Kutta methods. In contrast to existing SBP time integration
methods using simultaneous approximation terms to impose the initial condition
weakly, the new schemes use a projection method to impose the initial condition
strongly without destroying the SBP property. The new class of methods includes
the classical Lobatto IIIA collocation method, not previously formulated as an
SBP scheme. Additionally, a related SBP scheme including the classical Lobatto
IIIB collocation method is developed.

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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: stat