Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Stability Preserving Integrating Factor Two-step Runge--Kutta
  Methods   Problems that feature significantly different time scales, where the stiff
time-step restriction comes from a linear component, implicit-explicit (IMEX)
methods alleviate this restriction if the concern is linear stability. However,
where the SSP property is needed, IMEX SSP Runge-Kutta (SSP-IMEX) methods have
very restrictive time-steps. An alternative to SSP-IMEX schemes is to adopt an
integrating factor approach to handle the linear component exactly and step the
transformed problem forward using some time-evolution method. The strong
stability properties of integrating factor Runge--Kutta methods were previously
established, where it was shown that it is possible to define explicit
integrating factor Runge-Kutta methods that preserve strong stability
properties satisfied by each of the two components when coupled with forward
Euler time-stepping. It was proved that the solution will be SSP if the
transformed problem is stepped forward with an explicit SSP Runge-Kutta method
that has non-decreasing abscissas. However, explicit SSP Runge-Kutta methods
have an order barrier of p=4, and sometimes higher order is desired. In this
work we consider explicit SSP two-step Runge--Kutta integrating factor methods
to raise the order. We show that strong stability is ensured if the two-step
Runge-Kutta method used to evolve the transformed problem is SSP and has
non-decreasing abscissas. We find such methods up to eighth order and present
their SSP coefficients. Adding a step allows us to break the fourth order
barrier on explicit SSP Runge-Kutta methods; furthermore, our explicit SSP
two-step Runge--Kutta methods with non-decreasing abscissas typically have
larger SSP coefficients than the corresponding one-step methods.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: eess