应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2012年
1期
209-213
,共5页
分步单支theta方法%单边Lipschitz条件%均方稳定%非线性稳定
分步單支theta方法%單邊Lipschitz條件%均方穩定%非線性穩定
분보단지theta방법%단변Lipschitz조건%균방은정%비선성은정
Split-step one-leg theta methods%One-sided Lipschitz condition%Mean square stability%Nonlinear stability
本文研究随机微分方程单支theta方法的均方稳定性.首先,对线性检验方程,当0≤θ＜1时,分步单支theta方法在一定的步长限制下能保持原系统的均方稳定性,当θ=1时,方法按任意步长都能保持原系统的稳定性.其次,对满足单边Lipschitz条件的非线性随机微分方程,当1/2＜θo＜θ＜1时,方法能保持原系统的均方指数稳定性,但对步长有限制,如果θ=1,对步长限制消失.
本文研究隨機微分方程單支theta方法的均方穩定性.首先,對線性檢驗方程,噹0≤θ＜1時,分步單支theta方法在一定的步長限製下能保持原繫統的均方穩定性,噹θ=1時,方法按任意步長都能保持原繫統的穩定性.其次,對滿足單邊Lipschitz條件的非線性隨機微分方程,噹1/2＜θo＜θ＜1時,方法能保持原繫統的均方指數穩定性,但對步長有限製,如果θ=1,對步長限製消失.
본문연구수궤미분방정단지theta방법적균방은정성.수선,대선성검험방정,당0≤θ＜1시,분보단지theta방법재일정적보장한제하능보지원계통적균방은정성,당θ=1시,방법안임의보장도능보지원계통적은정성.기차,대만족단변Lipschitz조건적비선성수궤미분방정,당1/2＜θo＜θ＜1시,방법능보지원계통적균방지수은정성,단대보장유한제,여과θ=1,대보장한제소실.
In this paper,we are concerned with the mean-square stability properties of split-step one-leg theta methods for stochastic differential equations (SDEs).First,for a linear scalar test problem,the method with 0 ≤ θ＜ 1 preserves the mean-square stability of the test equation,but with a stepsize restriction,while the method with θ =1 well preserve the stability property without any constraints on the stepsize.Second,for nonlinear SDEs that have a negative one-sided Lipschitz constant,the method with 1/2 ＜ θo ＜ θ ＜ 1 can reproduce exponential mean-square stability properties under a restriction on stepsize.In the case θ =1,the restriction on stepsize disappears.
