@Article{JCM-40-177,
author = {Yuan , Haiyan},
title = {Convergence and Mean-Square Stability of Exponential Euler Method for Semi-Linear Stochastic Delay Integro-Differential Equations},
journal = {Journal of Computational Mathematics},
year = {2022},
volume = {40},
number = {2},
pages = {177--204},
abstract = {<p style="text-align: justify;">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&nbsp; 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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2010-m2019-0200},
url = {http://global-sci.org/intro/article_detail/jcm/20183.html}
}