Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Alternating Directions Implicit Integration in a General Linear Method
  Framework   Alternating Directions Implicit (ADI) integration is an operator splitting
approach to solve parabolic and elliptic partial differential equations in
multiple dimensions based on solving sequentially a set of related
one-dimensional equations. Classical ADI methods have order at most two, due to
the splitting errors. Moreover, when the time discretization of stiff
one-dimensional problems is based on Runge-Kutta schemes, additional order
reduction may occur. This work proposes a new ADI approach based on the
partitioned General Linear Methods framework. This approach allows the
construction of high order ADI methods. Due to their high stage order, the
proposed methods can alleviate the order reduction phenomenon seen with other
schemes. Numerical experiments are shown to provide further insight into the
accuracy, stability, and applicability of these new methods.

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The categories of this paper are: physics
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The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int