Weak order stochastic Runge-Kutta methods for 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
Cited 5

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

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Runge-Kutta methods for numerical solution of stochastic differential equations

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

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Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise

Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge--Kutta family

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Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge--Kutta family

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

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Weak first- or second-order implicit Runge-Kutta methods for stochastic differential equations with a scalar Wiener process

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Runge-Kutta Methods for the Strong Approximation of Solutions of 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 under a commutativity condition, which is derivative-free and which attains order 4 for ordinary differential equations. The weak order conditions are derived by utilizing multi-colored rooted tree analysis and a solution is found in a transparent way. The scheme is compared with other derivative-free and weak second order schemes in numerical experiments.