TY - JOUR
T1 - Strong Convergence of the Semi-Implicit Euler Method for a Kind of Stochastic Volterra Integro-Differential Equations
AU - Jianfang Gao, Shufang Ma & Hui Liang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 547
EP - 565
PY - 2018
DA - 2018/12
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2017-0030
UR - https://global-sci.org/intro/article_detail/nmtma/12908.html
KW - 
AB - <p style="text-align: justify;">This paper is mainly concerned with the strong convergence analysis of the semi-implicit Euler method for a kind of stochastic Volterra integro-differential equations (SVIDEs). The solvability and the mean-square boundedness of numerical solutions are presented. In view of the properties of the Itô integral, different from the known stochastic problems, it is proved that the strong convergence order of the semi-implicit Euler method is 1, although the approximation order of the Itô integral is 0.5. The theoretical results are illustrated by extensive numerical examples.</p>