Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Super-Convergent Implicit-Explicit Peer Methods with Variable Step Sizes   Dynamical systems with sub-processes evolving on many different time scales
are ubiquitous in applications. Their efficient solution is greatly enhanced by
automatic time step variation. This paper is concerned with the theory,
construction and application of IMEX-Peer methods that are super-convergent for
variable step sizes and A-stable in the implicit part. IMEX schemes combine the
necessary stability of implicit and low computational costs of explicit methods
to efficiently solve systems of ordinary differential equations with both stiff
and non-stiff parts included in the source term. To construct super-convergent
IMEX-Peer methods which keep their higher order for variable step sizes and
exhibit favourable linear stability properties, we derive necessary and
sufficient conditions on the nodes and coefficient matrices and apply an
extrapolation approach based on already computed stage values. New
super-convergent IMEX-Peer methods of order $s+1$ for $s=2,3,4$ stages are
given as result of additional order conditions which maintain the
super-convergence property independent of step size changes. Numerical
experiments and a comparison to other super-convergent IMEX-Peer methods show
the potential of the new methods when applied with local error control.

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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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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: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom