非线性随机延迟微分方程半隐式Euler方法的收敛性  

Convergence of semi-implicit Euler methods for nonlinear stochastic delay differential equations

作　　者：王文强[1] 李寿佛[1] 黄山[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《云南大学学报（自然科学版）》2008年第1期11-15,20,共6页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(10571147);湖南省教育厅资助项目(06B091);湖南省重点学科建设项目资助

摘　　要：首先利用附近已有节点上的值通过插值对延迟项进行数值逼近,然后针对较一般情形下的一类非线性随机延迟微分方程初值问题,得到了带线性插值的半隐式Euler方法在均方意义下是收敛的理论结果,它推广了已有文献中的相关结论.It is concerned with the error analysis of semi-implicit Euler methods applied to a general class of nonlinear stochastic delay differential equations. A new attempt to get the numerical approximation of the delay argument is presented,i, e, the delay argument is solved by interpolating. It is proved that the semi-implicit Euler methods with linear interpolation procedure is convergent. Moreover, the results can be regarded as a extension of the similar conclusions in the present documents.

关 键 词：非线性随机延迟微分方程 半隐式EULER方法 插值 收敛性 

分 类 号：O241.81[理学—计算数学]