Y. Komori (2007), Multi-colored rooted tree analysis of the weak order
conditions of a stochastic Runge-Kutta family, Applied Numerical Mathematics,
57 (2), 147-165.
Abstract
The aim of the present paper is to give a tractable way of seeking weak
order conditions of a stochastic Runge-Kutta family for stochastic differential
equations with a multi-dimensional Wiener process. This is accomplished
by an extension of the rooted tree analysis for ordinary Runge-Kutta methods.
As a result, weak order conditions can be obtained directly from diagrams
of multi-colored rooted trees. This new methodology will be of benefit
when high weak order conditions need to be sought.
Note
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Last updated: 2008/06/13