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General order conditions for stochastic partitioned Runge–Kutta methods

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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.

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Authors and Affiliations

  1. Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, 1433, Ås, Norway

    Sverre Anmarkrud

  2. Department of Mathematics and Computer Science, University of Southern Denmark, 5230, Odense M, Denmark

    Kristian Debrabant

  3. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Anne Kværnø

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  1. Sverre Anmarkrud
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  2. Kristian Debrabant
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  3. Anne Kværnø
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Correspondence to Kristian Debrabant.

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Communicated by David Cohen.

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Anmarkrud, S., Debrabant, K. & Kværnø, A. General order conditions for stochastic partitioned Runge–Kutta methods. Bit Numer Math 58, 257–280 (2018). https://doi.org/10.1007/s10543-017-0693-6

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