Convergence and stability of split-step ? methods for stochastic variable delay differential equations

被引：1

作者：

Bao, Xuezhong ^{[1
,3
]}

Hu, Lin ^{[2
]}

机构：

[1] Gansu Univ Polit Sci & Law, Lanzhou, Peoples R China

[2] Jiangxi Univ Sci & Technol, Coll Sci, Sch Artificial Intelligence, Ganzhou, Peoples R China

[3] Gansu Univ Polit Sci & Law, Lanzhou 730070, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2023年 / 100卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Stochastic variable delay differential equations; split-step theta method; local Lipschitz condition; strong convergence; mean square stability; BACKWARD EULER METHOD; THETA METHODS; S-ROCK;

D O I：

10.1080/00207160.2023.2173549

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a split-step theta algorithm is proposed for nonlinear stochastic variable delay differential equations. It is proved that the numerical solution obtained by the algorithm converges to the exact solution under the local Lipschitz condition. Moreover, it is shown that the numerical algorithm can maintain the mean square stability of the analytical solution for linear scalar equations. Finally, numerical experiments demonstrate the correctness of the theoretical algorithm.

引用

页码：1171 / 1192

页数：22

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