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 - <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>