非线性随机分数阶积分微分方程半隐式欧拉解的收敛性和稳定性  

Convergence and Stability of Semi-Implicit Euler-Maruyama Solution for Nonlinear Stochastic Fractional Integro-Differential Equations

作　　者：李晓卫 贾宏恩 郭平 LI Xiao-wei;JIA Hong-en;GUO Ping(School of Mathematical Sciences, Taiyuan University of Technology, Taiyuan 030024, China)

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2021年第1期6-12,共7页Journal of North University of China(Natural Science Edition)

摘　　要：主要对非线性随机分数阶积分微分方程半隐式欧拉方法的收敛性进行了针对性研究,证明了此类半隐式欧拉方法具有强一阶收敛性.此外,在精确解满足均方稳定性的前提下,研究了非线性随机分数阶积分微分方程半隐式欧拉解的均方稳定性,最后利用数值算例验证了数值解的收敛性.This paper is mainly concerned with the convergence analysis of the semi-implicit Euler-Maruyama(EM)method for the nonlinear SFIDEs.It is proved that the semi-implicit EM solution of SFIDEs shares strong first order sharp convergence.Furthermore,on the premise that the exact solution satisfies the mean-square stability,we researched the mean-square stability of the semi-implicit EM solution of the nonlinear SFIDEs.At last,some numerical examples were presented to demonstrate the convergence of the numerical solutions.

关 键 词：随机分数阶积分微分方程 半隐式欧拉方法 收敛性 均方稳定性 

分 类 号：O242.28[理学—计算数学]