一类随机分数阶微分方程隐式Euler方法的弱收敛性与弱稳定性  

WEAK CONVERGENCE AND WEAK STABILITY OF IMPLICIT EULER METHOD FOR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION

作　　者：王文强[1] 孙晓莉[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》2014年第2期153-162,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11271311;11171352)资助项目

摘　　要：本文主要研究了一类随机分数阶微分方程隐式Euler方法的弱收敛性与弱稳定性.首先构造了数值求解随机分数阶微分方程的隐式Euler方法,然后证明该方法是弱稳定的和1阶弱收敛的,文末给出的数值算例验证了所获得的理论结果的正确性.The authors mainly study the weak convergence and weak stability of implicit Euler method for stochastic fractional differential equation. In this paper, an implicit numerical method for the stochastic fractional differential equation is proposed, 1-order weak convergence and weak stability of the implicit Euler method are established. Finally, one numerical example is given. The theoretical results are also confirmed bv a numerical experiment.

关 键 词：随机分数阶微分方程 隐式Euler方法 弱收敛性 弱稳定性 

分 类 号：O241.8[理学—计算数学]