基于彩色树理论的2种三阶半隐式随机Runge-Kutta算法  

Two three-stage semi-implicit stochastic Runge-Kutta methods based on colored rooted tree theory

作　　者：袁玲[1] 朱晓临[1] 彭虎[1] 戴习民[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2013年第8期1013-1018,共6页Journal of Hefei University of Technology：Natural Science

基　　金：教育部科学技术研究重大资助项目(309017);安徽省自然科学基金资助项目(11013606M06);第38批留学回国人员科研启动基金资助项目(2010JYLH0322)

摘　　要：文章针对一般形式的Stratonovich型随机微分方程,运用彩色树理论,根据阶条件构造了2类一阶强收敛的三级半隐式型Runge-Kutta算法,即YZP1算法和YZP2算法。理论分析和数值试验表明,与现有的算法相比,这2种新算法具有更高的精度和更大的稳定区域。Two kinds of threestage semiimplicit stochastic RungeKutta methodsYZP1 algorithm and YZP2 algorithm are constructed with strong order p1.0 for the Stratonovich stochastic differen tial equations based on the colored rooted tree theory. The results of theoretical analysis and numeri cal test show that these two new methods are superior in stability and precision compared with the ex isting algorithms.

关 键 词：随机微分方程 彩色树 随机Runge-Kutta算法 均方稳定 

分 类 号：O241.8[理学—计算数学]