Y. Komori and K. Buckwar (2013), Stochastic Runge-Kutta methods with deterministic
high order for ordinary differential equations, BIT Numerical Mathematics,
53 (3), 617-639.
Abstract
We consider embedding deterministic Runge-Kutta methods with high order
into weak order stochastic Runge-Kutta (SRK) methods for non-commutative
stochastic differential equations (SDEs). As a result, we have obtained
weak second order SRK methods which have good properties with respect to
not only practical errors but also mean square stability. In our stability
analysis, as well as a scalar test equation with complex-valued parameters,
we have used a multi-dimensional non-commutative test SDE. The performance
of our new schemes will be shown through comparisons with an efficient
and optimal weak second order scheme proposed by Debrabant and Roessler
(2009).
Note
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Last updated: 2013/09/01