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Order Conditions of Stochastic Runge-Kutta Methods by B-Series

K. Burrage and P. M. Burrage
SIAM Journal on Numerical Analysis
Vol. 38, No. 5 (2001), pp. 1626-1646
Stable URL: http://www.jstor.org/stable/3062051
Page Count: 21
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Order Conditions of Stochastic Runge-Kutta Methods by B-Series
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Abstract

In this paper, general order conditions and a global convergence proof are given for stochastic Runge-Kutta methods applied to stochastic ordinary differential equations (SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to illustrate this theory.

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