Stochastic Runge-Kutta methods with deterministic high order for ordinary differential equations
Stochastic Runge-Kutta methods with deterministic high order for ordinary differential equations
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DOI：
10.1007/s10543-013-0419-3
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发表时间：
2011-09
影响因子：
1.5
通讯作者：
Y. Komori;E. Buckwar
中科院分区：
文献类型：
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作者：
Y. Komori;E. Buckwar
考虑将高阶确定性Runge-Kutta方法嵌入到求解非对易随机微分方程的弱阶随机Runge-Kutta(SRK)方法中。因此，我们得到了弱二阶SRK方法，它们不仅具有良好的实用误差性质，而且具有良好的均方稳定性。在我们的稳定性分析中，以及具有复值参数的标量检验方程中，我们使用了多维非对易检验SDE。我们的新方案的性能将通过与Debrabant和Röüler(Appl.诺默。数学课。59：582-594,2009)。
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 Rößler (Appl. Numer. Math. 59:582–594, 2009).