求解随机常微分方程的平均单支θ-方法  

AVERAGED ONE-LEG θ-METHOD FOR SOLVING RANDOM ORDINARY DIFFERENTIAL EQUATIONS

作　　者：何鼎 胡鹏[1] He Ding;Hu Peng(School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]中国地质大学(武汉)数学与物理学院,武汉430074

出　　处：《数值计算与计算机应用》2022年第1期49-60,共12页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11771163)资助。

摘　　要：本文针对随机常微分方程(Random ordinary differential equations)的路径近似提出了平均单支θ-方法.在单边Lipschitz条件下,得到该方法的路径收敛性,并研究了此类方法的B-稳定性,证明当θ∈[1/2,1],方法是B-稳定的.最后,{数值实验}验证了本文的结论.In this paper, the averaged one-leg θ-method is presented for the pathwise approximation of random ordinary differential equations. The pathwise convergence of the method is derived under the one-side Lipschitz condition. And then the B-stability of this method is investigated. It is shown that when the parameter θ∈[1/2,1], the method is B-stable. At last, some numerical experiments are provided to validate our conclusions.

关 键 词：随机微分方程 平均单支θ-方法 路径近似 收敛性 B-稳定性 

分 类 号：O241.81[理学—计算数学]