Second order Runge-Kutta methods for stratonovich stochastic differential equations

Andreas Rößler*

*Corresponding author for this work
29 Citations (Scopus)


The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m-dimensional Wiener process is studied. Therefore, a new class of stochastic Runge-Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge-Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge-Kutta schemes are calculated explicitly.

Original languageEnglish
JournalBIT Numerical Mathematics
Issue number3
Pages (from-to)657-680
Number of pages24
Publication statusPublished - 01.09.2007


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