Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations

Authors:
Yoshio Komori
Affiliations:
Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Iizuka 820-8502, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 6
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Weak order stochastic Runge-Kutta methods for commutative stochastic differential equations

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Weak second order S-ROCK methods for Stratonovich stochastic differential equations

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Abstract

A new explicit stochastic Runge-Kutta scheme of weak order 2 is proposed for non-commutative stochastic differential equations (SDEs), which is derivative-free and which attains order 4 for ordinary differential equations. The scheme is directly applicable to Stratonovich SDEs and uses 2m-1 random variables for one step in the m-dimensional Wiener process case. It is compared with other derivative-free and weak second-order schemes in numerical experiments.