TY - JOUR T1 - Convergence and Mean-Square Stability of Exponential Euler Method for Semi-Linear Stochastic Delay Integro-Differential Equations AU - Yuan , Haiyan JO - Journal of Computational Mathematics VL - 2 SP - 177 EP - 204 PY - 2022 DA - 2022/01 SN - 40 DO - http://doi.org/10.4208/jcm.2010-m2019-0200 UR - https://global-sci.org/intro/article_detail/jcm/20183.html KW - Semi-linear stochastic delay integro-differential equation, Exponential Euler method, Mean-square exponential stability, Trapezoidal rule. AB -

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 $\frac{1}{2}$ 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.