非线性随机延迟微分方程半隐式Euler方法的均方稳定性  

MEAN-SQUARE STABILITY OF SEMI-IMPLICIT EULER METHODS FOR NONLINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

作　　者：王文强[1] 黄山[1] 李寿佛[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：《数值计算与计算机应用》2008年第1期73-80,共8页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金资助项目(10571147);湖南省教育厅资助科研项目(06B091).

摘　　要：本文首先将数值方法的均方稳定性的概念MS-稳定与GMS-稳定推广到一般情形,然后针对一维情形下的非线性随机延迟微分方程初值问题,证明了如果问题本身满足零解是均方渐近稳定的充分条件,那么当漂移项满足一定的限制条件时,半隐式Euler方法是MS-稳定的且带线性插值的半隐式Euler方法是GMS-稳定的理论结果.In this paper, the authors investigated the mean-square stability of semi-implicit Euler methods for the nonlinear stochastic delay differential equations. At first, the both definitions of MS-stability and GMS-stability of numerical methods are developed from the linear scalar system to general case. And then, when the zero solution satisfies the sufficient condition of the mean square stability, we obtained several theoretical ruslts of semi-implicit Euler methods. If the drift term satisfies some restrictions, then semi-implicit Euler methods is MS-stable, moreover, semi-implicit Euler methods with linear interpolation procedure is GMS-stable.

关 键 词：非线性随机延迟微分方程 半隐式EULER方法 MS-稳定性 GMS-稳定性 

分 类 号：O241.8[理学—计算数学]