Stochastic Runge-Kutta methods with deterministic high order for ordinary differential equations

被引：7
|
作者：
Komori, Yoshio [1 ]
Buckwar, Evelyn [2 ]
机构：
[1] Kyushu Inst Technol, Dept Syst Design & Informat, Iizuka, Fukuoka 8208502, Japan
[2] Johannes Kepler Univ Linz, Inst Stochast, A-4040 Linz, Austria
来源：
BIT NUMERICAL MATHEMATICS | 2013年 / 53卷 / 03期
关键词：
Weak second order; Explicit method; Ito stochastic differential equation; Mean square stability; MEAN-SQUARE STABILITY; NUMERICAL SCHEMES; SYSTEMS;
D O I：
10.1007/s10543-013-0419-3
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
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 Roler (Appl. Numer. Math. 59:582-594, 2009).
引用
收藏
页码：617 / 639
页数：23
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