随机时滞微分方程的数值算法实现  

Numerical Simulation of Stochastic Differential Equations with Delay

作　　者：蔡利娇 黄东卫 郭永峰 谭建国 CAI Li-jiao;HUANG Dong-wei;GUO Yong-feng;TAN Jian-guo(School of Mathematical Sciences,Tiangong University,Tianjin 300387,China)

机构地区：[1]天津工业大学数学科学学院,天津300387

出　　处：《烟台大学学报（自然科学与工程版）》2021年第1期10-15,共6页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(11672207);天津市自然科学基金资助项目(17JCQNJC03800,17JCYBJC15700,18JCYBJC18900)。

摘　　要：主要研究了一类随机时滞微分方程数值模拟的算法及实现问题。在一类常见的随机时滞微分系统中,对系统的确定项采用四阶Rounge-Kutta法进行离散,对系统的随机项应用Milsteins方法进行离散,并对时滞项采用等比例估算其数值,运用Mathematica系统编写程序,实现此类随机时滞系统的数值模拟。最后将该程序应用于某些实例,得到的结果说明了程序的有效性。The algorithm and implementation of numerical simulation for a class of stochastic delay differential equations are studied.In a common class of stochastic differential systems with time delays,the fourth order Runge-Kutta is used to discrete the determinations of the system,the Milsteins method is used to discrete the random items of the system,and the time-delay items are estimated by equal proportion.We use Mathematica system in writing a program to realize the numerical simulation of such systems with time delays.And,the effectiveness of this program is reflected by being applied to some examples.

关 键 词：随机时滞微分方程 Mathematica系统 数值模拟 CHEN系统 

分 类 号：O242.1[理学—计算数学]