BIT Numerical Mathematics

, Volume 52, Issue 2, pp 437–455 | Cite as

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

  • Dominique Küpper
  • Anne Kværnø
  • Andreas RößlerEmail author


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.


Stochastic differential-algebraic equation Stochastic Runge-Kutta method Stiffly accurate Mean-square convergence Mean-square stability 

Mathematics Subject Classification (2000)

65C30 65L80 65L06 65L20 


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© Springer Science + Business Media B.V. 2011

Authors and Affiliations

  • Dominique Küpper
    • 1
  • Anne Kværnø
    • 2
  • Andreas Rößler
    • 3
    Email author
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  3. 3.Mathematisches InstitutAlbert-Ludwigs-Universität FreiburgFreiburgGermany

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