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Stochastic B-Series and Order Conditions for Exponential Integrators

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Numerical Mathematics and Advanced Applications ENUMATH 2017 (ENUMATH 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

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Abstract

We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential Runge–Kutta integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential Runge–Kutta integrators. The resulting general order theory covers both Itô and Stratonovich integration.

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Author information

Authors and Affiliations

  1. Hawassa University, Department of Mathematics, Hawassa, Ethiopia

    Alemayehu Adugna Arara

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

    Kristian Debrabant

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

    Anne Kværnø

Authors
  1. Alemayehu Adugna Arara
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  2. Kristian Debrabant
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  3. Anne Kværnø
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Corresponding author

Correspondence to Anne Kværnø .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

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Arara, A.A., Debrabant, K., Kværnø, A. (2019). Stochastic B-Series and Order Conditions for Exponential Integrators. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_37

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