Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic Structure of the Weak Stage Order Conditions for Runge-Kutta
  Methods   Runge-Kutta (RK) methods may exhibit order reduction when applied to stiff
problems. For linear problems with time-independent operators, order reduction
can be avoided if the method satisfies certain weak stage order (WSO)
conditions, which are less restrictive than traditional stage order conditions.
This paper outlines the first algebraic theory of WSO, and establishes general
order barriers that relate the WSO of a RK scheme to its order and number of
stages for both fully-implicit and DIRK schemes. It is shown in several
scenarios that the constructed bounds are sharp. The theory characterizes WSO
in terms of orthogonal invariant subspaces and associated minimal polynomials.
The resulting necessary conditions on the structure of RK methods with WSO are
then shown to be of practical use for the construction of such schemes.

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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int