Y. Komori (2004), Multi-Colored Rooted Tree Analysis of the Weak Order Conditions of a Stochastic Runge-Kutta Family under a Commutativity Condition, Technical Report CSSE-22, Faculty of Computer Science & Systems Engineering, Kyushu Institute of Technology.

Abstract
The present paper is aimed at multi-colored rooted tree analysis to give a transparent expression of weak order conditions of a stochastic Runge-Kutta family for stochastic differential equations satisfying a commutativity condition. As a result, a new explicit stochastic Runge-Kutta scheme is given, which is of weak order 2 and order 4 in the deterministic mean.

Note
The material in this report has been superseded by Y. Komori (2007).

The pdf file is obtainable from here.

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Last updated: 2007/03/26