CONVERGENCE AND MEAN-SQUARE STABILITY OF EXPONENTIAL EULER METHOD FOR SEMI-LINEAR STOCHASTIC DELAY INTEGRO-DIFFERENTIAL EQUATIONS  

作　　者：Haiyan Yuan 

机构地区：[1]Department of Mathematics,Heilongjiang Institute of Technology,Harbin 158100,China

出　　处：《Journal of Computational Mathematics》2022年第2期177-204,共28页计算数学（英文）

基　　金：This research is supported by National Natural Science Foundation of China(Project No.11901173);by the Heilongjiang province Natural Science Foundation(LH2019A030);by the Heilongjiang province Innovation Talent Foundation(2018CX17).

摘　　要：In this paper,the numerical methods for semi-linear stochastic delay integro-difFerential equations are studied.The uniqueness,existence and stability of analytic solutions of semi-linear stochastic delay integro-differential equations are studied and some suitable conditions for the mean-square stability of the analytic solutions are also obtained.Then the numerical approximation of exponential Euler method for semi-linear stochastic delay integro-differential equations is constructed and the convergence and the stability of the numerical method are studied.It is proved that the exponential Euler method is convergent with strong order 1/2 and can keep the mean-square exponential stability of the analytical solutions under some restrictions on the step size.In addition,numerical experiments are presented to confirm the theoretical results.

关 键 词：Semi-linear stochastic delay integro-differential equation Exponential Euler method Mean-square exponential stability Trapezoidal rule 

分 类 号：O24[理学—计算数学]