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A Runge-Kutta method for index 1 stochastic differential-algebraic equations with scalar noise

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Abstract

The paper deals with the numerical treatment of stochastic differential-algebraic equations of index one with a scalar driving Wiener process. Therefore, a particularly customized stochastic Runge-Kutta method is introduced. Order conditions for convergence with order 1.0 in the mean-square sense are calculated and coefficients for some schemes are presented. The proposed schemes are stiffly accurate and applicable to nonlinear stochastic differential-algebraic equations. As an advantage they do not require the calculation of any pseudo-inverses or projectors. Further, the mean-square stability of the proposed schemes is analyzed and simulation results are presented bringing out their good performance.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Dominique Küpper

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

    Anne Kværnø

  3. Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104, Freiburg, Germany

    Andreas Rößler

Authors
  1. Dominique Küpper
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  2. Anne Kværnø
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  3. Andreas Rößler
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Correspondence to Andreas Rößler.

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Communicated by Desmond Higham.

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Küpper, D., Kværnø, A. & Rößler, A. A Runge-Kutta method for index 1 stochastic differential-algebraic equations with scalar noise. Bit Numer Math 52, 437–455 (2012). https://doi.org/10.1007/s10543-011-0354-0

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  • DOI: https://doi.org/10.1007/s10543-011-0354-0

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