Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive high-order splitting methods for systems of nonlinear evolution
  equations with periodic boundary conditions   We assess the applicability and efficiency of time-adaptive high-order
splitting methods applied for the numerical solution of (systems of) nonlinear
parabolic problems under periodic boundary conditions. We discuss in particular
several applications generating intricate patterns and displaying nonsmooth
solution dynamics. First we give a general error analysis for splitting methods
for parabolic problems under periodic boundary conditions and derive the
necessary smoothness requirements on the exact solution in particular for the
Gray-Scott equation and the Van der Pol equation. Numerical examples
demonstrate the convergence of the methods and serve to compare the efficiency
of different time-adaptive splitting schemes and of splitting into either two
or three operators, based on appropriately constructed a posteriori local error
estimators.

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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: math-ph