BIT Numerical Mathematics

, Volume 37, Issue 4, pp 771–780 | Cite as

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

  • K. Burrage
  • P. M. Burrage
  • J. A. Belward


In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if ans-stage SRK contains Stratonovich integrals up to orderp then the strong order of the SRK cannot exceed min{(p+1)/2, (s−1)/2},p≥2,s≥3 or 1 ifp=1.

AMS subject classification


Key words

Stochastic ordinary differential equation Runge-Kutta methods strong order 


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Copyright information

© Swets & Zeitlinger 1997

Authors and Affiliations

  • K. Burrage
    • 1
  • P. M. Burrage
    • 1
  • J. A. Belward
    • 1
  1. 1.Department of MathematicsThe University of QueenslandBrisbaneAustralia

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