General order conditions for stochastic partitioned Runge-Kutta methods

Sverre Anmarkrud, Kristian Debrabant, Anne Kværnø

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Abstract

In this paper stochastic partitioned Runge-Kutta (SPRK) methods are considered. A general order theory for SPRK methods based on stochastic B-series and multicolored, multishaped rooted trees is developed. The theory is applied to prove the order of some known methods, and it is shown how the number of order conditions can be reduced in some special cases, especially that the conditions for preserving quadratic invariants can be used as simplifying assumptions.
Original languageEnglish
JournalBIT Numerical Mathematics
Volume58
Issue number2
Pages (from-to)257–280
ISSN0006-3835
DOIs
Publication statusPublished - 2018

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Keywords

  • math.NA
  • 65C30, 60H35, 65C20

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